Karzai announced plans for the high-level talks during an appearance on CNN's Situation Room on Monday.
During those talks, President Obama and Zadari were unable to reach a last-minute deal to reopen critical U.S. supply routes to Afghanistan that run into Pakistan.
Indications coming out of Islamabad prior to the NATO summit was a deal to open the routes was all but complete. The lines had been shut off to American and coalition forces since last November.
But a Pakistani demand to increase the price-per-truck cost to the United States to move through supplies through the country, as well as other issues, eventually brought negotiations to a halt.
DOD spokesman George Little on Tuesday re-emphasised the need to get those Pakistani supply lines up and running.
The lines will be critical in getting weapons and supplies to American and NATO forces as they begin their spring offensive against Taliban strongholds in Eastern Afghanistan, Little told reporters during Tuesday's briefing at the Pentagon.
But those lines will be equally as important in moving tons of U.S. equipment and material out of Afghanistan as American and coalition commanders prepare to withdraw from the country in 2014.
Little acknowledged the "financial side of the equation" regarding Pakistan's plans to increase the per-truck fee for American forces to use the supply lines was something both sides "have to get past."
Aside from supply lines, Karzai and Gilani also plan to tackle the politically-sensitive issue of suspected terrorist safe havens along the Afghan-Pakistan border.
Members of the Haqqani network, a Pakistan-based terror group affiliated with the Taliban, continue to stage attacks against American troops in Afghanistan from these havens across the border in Pakistan.
Those cross-border raids are a main reason why eastern Afghanistan is being targeted as the main objective for U.S. and coalition forces during this summer’s fighting season.
Afghanistan and Pakistan are "in a dialogue" to eliminate these cross-border terror outposts in Pakistan, according to Karzai.
"We hope this dialogue will move forward that will result in the removal of terrorists from Pakistan," Karzai said on Monday. "We are working toward a constructive relationship with Pakistan in [these] areas."
Noting the Haqqani network's presence along the Afghan border is an issue that the "Pakistani government will not deny," Karzai reiterated that both countries continued to make progress on the issue.
"The difference is today is that we are talking about these issues more openly and in a friendlier environment than we have before," the Afghan president said. "In keeping with this environment, we hope to find solutions."