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.
BBC: British soldier killed by Afghan army gunman in Helmand
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.
And could tainted relations between the two countries even have robbed Ani of victory at Eurovision 2008?
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?
WHITEHOUSE: President Obama and President Santos Hold a Press Conference | The White House
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.
The talks were aimed at rebuilding relations between the two countries after the spat over the U.S.-led war on Iraq.
U.S. President Barack Obama and Castro spoke on the phone Friday to discuss the process of normalizing relations between the two countries.
Donald Rumsfeld, the US Defence Secretary and Bush administration geopolitical hit-man, said that relations between the two countries had been poisoned.
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
Relations between the two countries had been frosty since 24 Pakistan soldiers were killed in a Nato air strike in November 2011.
He is convinced that if economic relations between the two countries were to cool it would be bad for both of them.
Relations between the two countries have been fraught over the past several decades and the neighbours have fought three wars since 1947.
BBC: India's SM Krishna to seek speedy Pakistan Mumbai trial
The issue of cyber hacking has strained relations between the two countries.
But broader relations between the two countries were never quite so bad.
ECONOMIST: German-American relations: Ready for a Bush hug? | The
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.
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