Ukraine's ousted pro-Moscow president Viktor Yanukovych has emerged defiant after five days in hiding.
Mr Yanukovych is to hold a press conference in Russia tomorrow, in his first public appearance since fleeing Ukraine at the weekend.
It comes as Ukraine's new leaders issued a blunt warning to Russia against any aggression on the volatile Crimean peninsula.
Meanwhile the White House dismissed Mr Yanukovych's assertion that he is still the Ukraine's president, and reinforced US warnings to Russia that it must avoid "miscalculations" in military drills along the border of troubled Ukraine.
The comments, which built upon statements by US Defense Secretary Chuck Hagel, appeared to reflect Washington's concern that Russian drills near the ex-Soviet state could trigger events which may get out of control.
"We are closely watching Russia's military exercises along the Ukraine border," said White House spokesman Jay Carney.
"We expect Russia to be transparent about these activities and to avoid provocative actions," Carney said, adding that Moscow should not take steps that could be misinterpreted or lead to "miscalculations during a very delicate time."
Russia ordered military exercises earlier this week, as political tensions in the region soared following the ousting of the Russian-backed president of Ukraine Viktor Yanukovych.
Hagel had earlier said at NATO meetings in Brussels that Russia needed to be transparent about its activities and used language later echoed by Carney.
The White House also welcomed the decision by Ukraine's parliament to name a new government under Prime Minister Arseniy Yatsenyuk.
