The diplomatic maneuvers come as world leaders meet in Paris for talks that were intended to focus on Lebanon.
Instead, Ukraine will likely dominate the agenda.
Russian forces remain in effective control of Crimea, a Black Sea peninsula where Russia has a huge naval base, in a tense standoff with Ukrainian forces loyal to the new interim government in Kiev.
Russia has been warned that possible sanctions will be on the agenda when EU leaders meet Thursday if no progress is made in ending the high-stakes showdown.
U.S. Secretary of State John Kerry and his Russian counterpart Sergey Lavrov are due to have talks.
But UK Foreign Secretary William Hague said what happens at the EU meeting on sanctions "will be partly determined by Russia's willingness to sit down with Ukraine."
If no progress can be made on de-escalating the situation, then there will be "costs and consequences," he said.
"It will be a test this afternoon of whether Russia is prepared to sit down with Ukraine. And we will strongly recommend that they do so."
Hague's comments came after he, Kerry and Ukrainian Foreign Minister Andrii Deshchytsia discussed their next steps ahead of Lavrov's expected arrival in the French capital.
Kerry reminded Moscow that it had, like Washington and London, signed an agreement in 1994 when Ukraine agreed to give up nuclear weapons "to refrain from the threat or use of force against the territorial integrity or political independence of Ukraine."
This means there are "very clear legal obligations that are at risk in this," he said.
The Kremlin earlier threatened to hit back if the European Union does levy sanctions against Russia.
Russian lawmakers are drafting a law that will allow Russia to confiscate assets belonging to U.S. and European companies if it faces sanctions.
Andrei Klishas, a senior lawmaker in the upper house, said the bill "would offer the president and government opportunities to defend our sovereignty from threats," state news agency RIA Novosti reported.
France: Invasion violates international law
The tit-for-tat threats are the latest in a war of words over Russia's military intervention in Ukraine's southern Crimea region.
On Tuesday, a defiant Russian President Vladimir Putin denied Russian troops were in Crimea but reserved the right to take military action to protect the safety of ethnic Russians in eastern Ukraine.
He also slammed the interim government, which replaced ousted Ukrainian President Viktor Yanukovych, a Russian ally, as illegitimate.
French Foreign Minister Laurent Fabius set out a very different point of view Wednesday as he declared that sanctions could be on the cards.
"The invasion of one country into another is contrary to all international laws. We must return to dialogue and to bear in mind that Ukraine should work with Russia and the EU," he said via Twitter.
"We cannot accept, we members of the international community, a country that invades another."
On Tuesday, Kerry accused Russia of making up reasons for intervention in Ukraine, saying "not a single piece of credible evidence supports any one of these claims."
NATO members are set to meet with Russia's ambassador to the alliance Wednesday, amid concerns that the crisis could spread, and Swedish Foreign Minister Carl Bildt will meet with his Danish and Norwegian counterparts in Ukraine's capital, Kiev, he said on Twitter.
EU Commission President Jose Manuel Barroso announced in Brussels Wednesday the EU would would offer an aid package worth 11 billion euro to Ukraine.
He said the package was "designed to assist a committed, inclusive and reforms oriented" Ukrainian government.
Barroso confirmed on Twitter that the aid package would consist "of immediate short and medium term measures offering trade, economic, technical and financial assistance to #Ukraine."
During his visit to Kiev on Tuesday, Kerry announced the United States will give Ukraine's new government a $1 billion loan guarantee.
Senior U.S. administration officials told CNN this would help insulate the Ukrainian economy from the effects of reduced energy subsidies from Russia.
German Chancellor Angela Merkel is trying to construct what a senior U.S. administration official characterized as an "off-ramp" for Putin by having international observers in Crimea to ensure ethnic Russians' rights aren't violated.
President Barack Obama floated this idea in a call Saturday with Putin, and he and Merkel talked about it Tuesday.
Lavrov: Military coup in Ukraine
Lavrov, speaking in Madrid Wednesday morning, showed no signs of budging from the position taken by Putin a day earlier.
The Russian foreign minister said the crisis had begun when the international community failed to react to the anti-government protests that preceded Yanukovych's ouster.
"There was a military coup and the legitimate president was removed by methods which were not in the constitution or legislation," Lavrov said.
"If we are so lenient to the people who are trying to govern our neighbor, everyone must realize a bad example can be spread and there shouldn't be any double standards."
Lavrov repeated Putin's denial that Russian troops are in control in Crimea, saying that the troops in question are "self-defense" forces over whom Russia has no control.
Decisions on whether international observers should be sent into Ukraine are for leaders in the country to make, he said.
He pointed out that the newly installed pro-Russian government in Crimea does not see the authorities in Kiev as legitimate.
"This problem is multi-faceted. In order to calm the situation down everyone must act in accordance with the law," he said.
Stability fears Tuesday's diplomatic efforts bore little fruit.
But some observers saw a positive sign in Putin ordering Russian troops who were on mass military exercises close to the border with Ukraine back to their bases.
No violence has yet erupted in Crimea, where Russian troops currently control military bases and key installations, but the situation remains volatile.
Andriy Parubiy, secretary of Ukraine's Security and Defense Council, told reporters in Kiev Wednesday that the situation in Crimea was more calm than it was a day earlier.
Parubiy said Russian forces had not made any new military gains on the peninsula but warned of the danger of new attempts by pro-Russian protesters to take over government buildings in eastern and southern Ukraine.
Warning shots were fired by the Russia side during a confrontation at a military base near the port of Sevastopol Tuesday with Ukrainian forces, before the situation was defused.