Friday's clashes culminated in a major fire at a trade union building where most of the deaths occurred.
Hundreds of people gathered there on Saturday.
The protest comes as Ukraine says it has seized a security building from rebels in the east of the country.
Seven international monitors held by pro-Russian activists in eastern Ukraine were released earlier.
US Secretary of State John Kerry and his Russian counterpart, Sergei Lavrov, have again spoken by phone about the crisis.
Mr Lavrov urged Mr Kerry to put pressure on Kiev to stop its military operation, which he said risked "plunging the country into a fratricidal conflict".
Mr Kerry said Moscow should stop backing the pro-Russian separatists.
Both men also discussed the possibility of greater involvement by the Organization for Security and Co-operation in Europe (OSCE) in trying to find a solution to the crisis.
The violence in Odessa was the most serious in Ukraine since February when more than 80 people were killed during protests in Kiev against the ousted President Viktor Yanukovych.
Groups sympathetic to Russia, some armed, are reported to have attacked a larger protest against separatism.
Skirmishes between the two groups then broke out in several parts of the south-western city.
Pro-Russia protesters are later said to have sought refuge in the trade union building after their encampment was burned down.
Petrol bombs were thrown leading to the deaths of at least 36 people inside, according to official figures.
The blackened trade union building, its windows broken, was ringed by police on Saturday as the crowd assembled.
Some laid flowers; others chanted pro-Russian slogans.
There were isolated scuffles between rival groups and Ukrainian flags were burned or bundled away.
Early on Saturday, the Kiev government resumed military action against Russian separatists in the east of the country, with fighting reported in some areas.
In Kramatorsk, south of rebel-held Sloviansk, Ukrainian forces recaptured the headquarters of the SBU security service from pro-Russian separatists, according to the interior ministry.
But in Luhansk, pro-Russian gunmen have stormed a building housing a regiment of interior ministry troops, local officials say.
The defence ministry also reported "serious fighting" on Friday night in Andreevka, some 6km (4 miles) west of rebel-held Sloviansk, with two Ukrainian soldiers killed.
Ten separatists died in Andreevka, a spokeswoman for the pro-Russian force in Sloviansk said.
The seven international military observers, whose release emerged early on Saturday, were captured a week ago and held in Sloviansk.
Five Ukrainian officers captured with the observers, who are linked to the OSCE, were also released.
Pro-Russian separatists in Sloviansk say they released the observers "without conditions".
"As I promised them, we celebrated my birthday yesterday and they left. As I said, they were my guests," the self-proclaimed mayor of Sloviansk, Vyacheslav Ponomaryov, said.
Russia had sent an envoy to negotiate the releases.
Vladimir Lukin said he hoped the "voluntary act" by the separatists would be reciprocated by Kiev, adding:
"I would very much like military actions to end."
One of the observers, German Col Axel Schneider, said the team had been treated "as good as possible" in what was a "miserable situation".
Western leaders had condemned the abductions.
The observers - four Germans, a Dane, a Pole and a Czech - are not part of the main OSCE monitoring mission, which was agreed after long negotiations by Russia, Ukraine and the US.
A second day of military operations is under way to try to reassert central control here in eastern Ukraine and in particular in the city of Sloviansk, which has become the stronghold of pro-Russian groups.
Ukraine's interior minister has been saying "we will not stop" - suggesting that, unlike in the past when Ukrainian troops have moved in and then withdrawn, these operations will continue.
The interior ministry is also very angry that Moscow has been talking of Kiev carrying out "punitive actions" in the east and that it has been firing on civilians.
The government in Ukraine is anxious that it does not give any pretext for Russia to send in its troops.
That pretext would be that civilians - Russian-speaking citizens - were in danger and needed protection.
Pro-Russian groups have spoken again of needing peacekeeping troops.
That would include Russians coming in to protect civilians - obviously something Kiev wants to avoid.
Source: BBC News Europe