Diplomatic efforts to bring the Taliban to the negotiating table have gained pace recently, even as security forces have launched offensives against the insurgent group without NATO assistance for the first time since 2002.
Ghani and Abdullah leave tomorrow for an official four-day trip to Washington, where the president will address a joint session of Congress. Both men will then visit Camp David and New York.
Besides the US, Ghani also visited Saudi Arabia this week, while Abdullah was in India to try to obtain a "regional consensus" on reconciliation with the Taliban, according to Afghan officials.
"One of the factors which is motivating President Ghani to act now could be trying to make as much progress as possible before the fighting season begins, but it's not the only factor," said a Western diplomat.
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The visit will also include an economic component, with planned discussions on the future of cooperation between the two countries.
A senior Afghan official who requested anonymity told AFP: "The meetings in the US will focus on another key point: the financial support to Afghanistan, which has been secured until 2017, but needs to be confirmed for the following five years.
The trip is also seen as an important step toward mending relations between the US and Afghanistan, which deteriorated towards the end of former President Hamid Karzai's ten-year rule.
"The first goal to achieve is the rehabilitation of the relationship with the USA. US-Afghanistan relations were tough during the past government," Javid Faisal, a spokesman for Abdullah told AFP.
Since coming to power in September, Ghani has focused on improving relations with neighbouring Pakistan, a key partner in the peace process, which his predecessor had refused to do.
"President Ghani is trying to establish a peace process, trying to begin talks... He recognises that in order for that to happen it will be important to have a new relationship with Pakistan and to build closer ties with China, Saudi Arabia, and to some extent the United Arab Emirates," said the Western diplomatic source.