Obasanjo, the current chairman of the African Union, conferred with US Secretary of State Condoleezza Rice at his hotel and was due to meet with President George W. Bush at the White House.
The Nigerian leader had said he hoped to brief Bush on his peace-making efforts in Togo, Ivory Coast and Sudan as well as pushing Nigeria's own case for the cancellation of its 35 billion-dollar external debt.
But, on the eve of his arrival, the US House of Representatives passed a resolution urging Obasanjo to rescind Liberian former president Taylor's political asylum in Nigeria and hand him over to international prosecutors at the war crimes tribunal in Sierra Leone.
There was no word on the substance of Rice's talks with Obasanjo but the meeting was also attended by the US ambassador for war crimes issues, Pierre-Richard Prosper, reporters at the hotel said.
Obasanjo has long insisted that he cannot go back on his word to Taylor and that he would only send him back to Liberia rather than neighbouring Sierra Leone and then only if October's Liberian elections produce a stable democratic regime which could build a case against him.
"Mr. Taylor is here because the international community collectively asked Mr. President to invite him in order to end the fighting," Obasanjo's spokeswoman Remi Oyo told AFP this week. "On October 11, the people of Liberia will be going to elections."
Taylor was removed to Nigeria in August 2003 after Obasanjo and other African leaders persuaded him to step down from office and allow a UN-backed interim government to bring an end to Liberia's latest bout of civil war and to begin organising proper elections.
But prosecutors have been agitating for him to be turned over to the UN-endorsed tribunal in Sierra Leone to face charges that he helped train and finance the rebel forces which committed large-scale atrocities during that west African country's own 1991-2001 civil war.
Taylor was indicted by the tribunal in June 2003 on a charge that he was the main backer of the rebel Revolutionary United Front, a ruthless guerrilla army funded by money from the diamond trade which waged a campaign of terror against civilians and was notorious for severing the limbs of its victims.
Last week, the outgoing chief prosecutor at the Sierra Leone court, former US Defence Department lawyer David Crane, accused Taylor of seeking to further destabilise west Africa by ordering the assassination of Guinea's President Lansana Conte.
Obasanjo's spokeswoman expressed doubt about the allegation. "In the beginning there was some flexing of muscles by him, then we put him in his place," she said. "When there's an elected government in Liberia and it asks for him, he will go. He is not Nigerian."
Wednesday US lawmakers urged Nigeria to transfer Taylor "to the jurisdiction of the Special Court for Sierra Leone to undergo a fair and open trial for war crimes, crimes against humanity, and other serious violations of international humanitarian law."
The White House has not yet reacted to the House of Representatives' vote and the Bush administration has enjoyed good relations with Nigeria, which it sees as key to the stability of Africa's richest oil producing region.