Obama says US and Russia must unite to end North Korean and Iranian nuclear efforts.
Biden assured Yushchenko that US attempts to renew relations with Russia would “not come at Ukraine’s expense”.
Yushchenko, who came to power after a pro-Western revolution in 2004 in which he benefited from US support, told Biden that US-Ukrainian relations should be developed in a “constructive way”.
He said his country had chosen “a European path”, where “democracy rules”, in an apparent dig at Russia.
Biden’s comments come just two weeks after Barack Obama, the US president, visited Moscow in an effort to strengthen ties between the two former Cold War enemies.
Neave Barker, Al Jazeera’s correspondent in Moscow, said: “There’s been a clear signal from the White House that by sending the vice-president and by overlooking a presidential visit to Kiev, it’s set on indicating how much the Obama administration value the need to reset ties with Russia.
“The Obama administration know they are walking a political tightrope, on the one hand wanting to maintain workable relations with post-Soviet nations in Eastern Europe, but at the same time wanting to restore a new level of ties with Russia.
“I think this meeting doesn’t go any further than touching base between Ukraine and the Obama administration.
“There are much more pressing concerns in Ukraine at the moment than joining Nato … the country is deep in recession … and needs financial support from the US.”
‘Spheres of influence’
Russia strongly opposes Ukraine’s bid to join Nato, seeing it as an attempt by the West to move on its sphere of influence.
Biden said in his speech: “We don’t recognise, and I want to reiterate this, any spheres of influence.”
The US vice-president will later meet Yulia Tymoshenko, Ukraine’s prime minister.
Tymoshenko and Yushchenko, allies in the 2004 Orange Revolution that brought the president to power, are now enemies after disagreeing over a number of issues, including Ukraine’s relations with Russia.
Biden will also meet Viktor Yanukovych, Ukraine’s main opposition leader, who has been depicted as having a friendlier attitude towards Moscow than the president.
Yushchenko told Biden that Ukraine would like the US to help finance the modernisation of its gas transit network, which he called “an integral part of the European gas market”.
The US vice-president will head to Georgia to meet Mikheil Saakashvili, the country’s president, on Wednesday.
Georgia also wishes to join Nato and currently has strained relations with Moscow following its war with Russia last year over the breakaway Georgian regions of Abkhazia and South Ossetia.