Diplomatic and trade relations between the two countries now ride on the fate of the extradition bill.
Venezuela's foreign minister said the meeting would "derail" good relations between the two countries.
Relations between the two countries have been strained, most recently over the conflict in Syria.
The visit comes in the backdrop of recent tense relations between the two countries.
Since the start of the Bush administration, relations between the two countries have worsened.
Relations between the two countries have stabilised, but the lack of trust remains deep.
Relations between the two countries have been strained over their support for opposing sides in Afghanistan.
Correspondents say relations between the two countries have been more fractious than usual in recent months.
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His trip to Washington comes at a crucial time for relations between the two countries.
Still, these are tense and unpredictable times in trade relations between the two countries.
Relations between the two countries have warmed since Libya dropped its nuclear-weapons programme in 2003.
Mr Karzai's trip to Washington comes at a crucial time for relations between the two countries.
President Richard Nixon visited China in 1972, and relations between the two countries were normalized in 1979.
Or can we interpret it as a new phase beginning in the relations between the two countries?
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Relations between the two countries are strained following a border dispute, which makes dealing with common problems difficult.
Correspondents say the move to resume cricketing ties is a sign of improving relations between the two countries.
U.S. President Barack Obama and Raul Castro spoke on the phone Friday to discuss the process of normalizing relations between the two countries.
Venezuelan authorities have deported an alleged top Farc guerrilla to Colombia, in the latest sign of improving relations between the two countries.
Relations between the two countries had recently deteriorated to the point of playground insults, but leaders were on this occasion more statesmanlike.
ECONOMIST: A powwow, but the chief troublemakers are not invited
He is convinced that if economic relations between the two countries were to cool it would be bad for both of them.
The issue of cyber hacking has strained relations between the two countries.
But broader relations between the two countries were never quite so bad.
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In 2008 and 2011, Thailand and Cambodia fought brief border wars that claimed scores of lives and strained relations between the two countries.
In August of that year, Albright's move was regarded by then-President Mohammad Khatami as "a missed opportunity" to normalize relations between the two countries.
He had been trying to coax life back into the once successful but now stagnant diplomatic effort to normalise relations between the two countries.
The zone is seen as a litmus-test of relations between the two countries, and analysts consider such an extended shut-down to be a considerable setback.
BBC: South Korea 'to withdraw staff' from Kaesong zone in North
Ashfaq Parvez Kayani in Brussels for talks that aimed to improve relations between the two countries and to bring the Taliban to the negotiating table.
Ashfaq Parvez Kayani in Brussels for talks that sought to both improve relations between the two countries and bring the Taliban to the negotiating table.
In Russia, however, reactions to Obama's election victory have been muted at a time when relations between the two countries are near Cold War levels.
The dispute is still unresolved and some fear that it may blow up again in the coming months and further hurt trade relations between the two countries.
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