Following the ouster of former President Viktor Yanukovych, Turchinov said more time is needed to allow for further consultations on the election of a new government, Voice of America reported.
The Legislature is scheduled to unveil its new leaders Thursday, CNN reported.
Meanwhile, Konstantin Khivrenko, the head of the country's electoral commission, said the campaign to elect a new president would begin Tuesday with elections taking place May 25.
The White House said Tuesday it no longer saw Yanukovych as Ukraine's active president and threw its support behind Turchinov, who was elected by Parliament.
"As you know, Mr. Yanukovych has left Kiev in an orderly fashion -- packed up his things and left -- and his whereabouts are not known to us in a confirmable way," White House spokesman Jay Carney told reporters in Washington.
"And certainly, while he was a democratically elected leader, his actions have undermined his legitimacy and he is not actively leading the country at present," he said.
Ukraine's acting government Monday declared Yanukovych a fugitive sought for mass murder in the bloody clashes between protesters and riot police a week ago that led to the deaths of at least 82 people, including 13 police officers, and more 1,100 injuries.
Yanukovych vanished Sunday night, driving off in a three-car convoy and severing all communication.
He was impeached by Parliament Saturday, a day after he signed a compromise deal with opposition leaders, envisaging a new national unity government, constitutional changes to hand powers back to Parliament and early elections to be held by December.
Yanukovych has officially been refused permission to fly out of Ukraine. He has said he will not resign.
Carney said the Obama administration considers the Ukrainian Parliament to have lawfully elected parliamentary Speaker Turchinov as the country's interim president.
"We encourage the Ukrainian Parliament and others to take actions that help continue a path toward de-escalation of violence, embrace constitutional change and move toward a coalition government -- a multiparty coalition government -- as well as early elections," he said.
Russian Prime Minister Dmitry Medvedev took exception to the U.S. characterization of Ukraine's embryonic government, sharply questioning its legitimacy.
"If you consider people roaming Kiev in black masks and Kalashnikov rifles to be a government, then it will be difficult for us to work with such a government," Medvedev told reporters in Sochi.
"Some of our foreign, Western partners think otherwise, considering them to be legitimate authorities," he said in remarks posted on the Russian government website.
"I do not know which constitution, which laws, they were reading," Medvedev said. "But it seems to me it is an aberration [that] something that is essentially the result of a mutiny is called legitimate."
Medvedev said the turmoil in Ukraine poses a serious threat to Russia's interests.
"It is not clear to us what is going on in the country and there is a real threat to our interests," he said.
Carney said the Obama administration was ready and willing to help Ukraine regain social and economic stability by providing support that would go beyond International Monetary Fund assistance being worked out among Western governments.
"This support can complement an IMF program by helping to make reforms easier and by putting Ukraine in a position to invest more in health and education, to help develop Ukraine's human capital and strengthen its social safety net," he said.