Senior Western diplomats are continuing talks in Kiev with the interim leadership, while the US and UK are to discuss emergency financial assistance.
The US has yet to endorse the new leader, but says "Mr Yanukovych is no longer actively leading the country".
An arrest warrant has been issued for Mr Yanukovych, who has disappeared.
Acting Interior Minister Arsen Avakov said a criminal case had been opened against the ousted president and other officials over "mass murder of peaceful citizens".
Mr Yanukovych was last reported seen on Sunday in Balaklava on the Crimean peninsula - an autonomous region where the majority of the population is ethnically Russian.
Dozens of people were killed in clashes between anti-Yanukovych protesters and riot police last week.
British investigators have told the BBC they are operating on the ground in Ukraine to help establish who was responsible for the most deadly day of violence last Thursday.
They say they are gathering evidence which could be used to prosecute suspects.
They refused to reveal their identities or who had tasked them with the investigation, saying it was a politically sensitive issue.
Mr Turchynov has promised that his coalition administration will be a "government of the people".
His ally, former PM Yulia Tymoshenko, who was released from jail on Saturday, has ruled out becoming prime minister.
But her spokeswoman said she had not yet decided whether to run for the presidency.
In the eastern city of Kharkiv, where Mr Yanukovych has enjoyed support, the head of the regional state administration has said he will run for the presidency.
Speaking on Kanal 5 TV, he gave as his reason "the fact that a total attack on the rights of the Russian-speaking population is under way, that laws are being adopted that threaten all those who do not accept fascism and Nazism".
Mr Dobkin has been under pressure from local demonstrators to quit.
On Monday, Russia issued its strongest response yet to the ousting of Mr Yanukovych, questioning the legitimacy of the Western-leaning interim leadership.
Prime Minister Dmitry Medvedev said they had conducted an "armed mutiny".
White House official Jay Carney said on Monday that although Mr Yanukovych "was a democratically elected leader, his actions have undermined his legitimacy, and he is not actively leading the country at present''.
Unrest in Ukraine began in November when Mr Yanukovych rejected a landmark association and trade deal with the EU in favour of closer ties with Russia.
Meanwhile, UK Foreign Secretary William Hague is to meet US Secretary of State John Kerry in Washington later to discuss emergency financial assistance to Kiev.
Mr Hague has warned that Ukraine faces imminent economic collapse without support from the international community.
The US has already said it is ready to give financial support to Ukraine to complement any future loan from the International Monetary Fund (IMF).
Ukraine is facing bankruptcy and further promised loans from Russia are looking increasingly unlikely.
EU foreign affairs chief Catherine Ashton remains in Kiev to discuss financial and political support for Ukraine's new leaders.
On Monday she visited Independence Square - the scene of deadly clashes between protesters and police - and held talks with Mr Turchynov.
Senior US officials, including Deputy Secretary of State William Burns, will join EU officials in Kiev to participate in two days of meetings with political, business and civil society leaders.
Western leaders, including French President Francois Hollande and German Chancellor Angela Merkel, have sent written appeals to Russian President Vladimir Putin to urge a peaceful transition in Ukraine.
Crimea and some pro-Russian areas in the east have seen protests against the overthrow of Mr Yanukovych, sparking fears that Ukraine could be split apart by separatist movements.
Thousands of people remain in Kiev's Independence Square, the Maidan.
Who is running Ukraine?
- Olexander Turchynov - deputy leader of the Fatherland party and a long-time opponent of Mr Yanukovych; appointed interim president
- Arsen Avakov - also a key Fatherland MP, now interim interior minister
- Arseniy Yatsenyuk - parliamentary leader of Fatherland and the main negotiator during Maidan protests; tipped as a possible future prime minister
- Vitali Klitschko - boxer turned politician who was a leading figure in the Maidan; heads Ukrainian Democratic Alliance for Reforms (Udar); expected to run for presidency
- Oleh Tyahnybok - leader of far-right Svoboda (Freedom) party; key Maidan protest leader
- Yulia Tymoshenko - former prime minister and opponent of Mr Yanukovych; released from jail as opposition took control of parliament; has ruled out running for PM
- 21 Feb: leaves Kiev for Kharkiv on helicopter; stays overnight in state residence
- 22 Feb: flies by helicopter to Donetsk airport; tries to leave on private jet but stopped by border guards; leaves by car for Crimea
- 23 Feb: arrives in Balaklava, Crimea, and stays briefly in a private spa before making aborted attempt to reach Belbek airport
- Dismisses most of his security detail; leaves Balaklava in a three-car convoy with some guards and ex-presidential administration head Andriy Kluyev
Source: BBC News