A top Obama Administration official has described Karzai's scheduled visit to India later this week visit as important from the perspective of the US.
"His upcoming visit to India could, I think, be quite influential because he highly respects and has good relations with the Indian government," James Dobbins, the US Special Representative for Afghanistan and Pakistan, told members of the powerful Senate Foreign Relations committee.
US President Barack Obama had personally sought Indian help when he met Prime Minister Manmohan Singh at the White House in September.
Following the meeting, National Security Advisor Shivshankar Menon had a separate meeting with his US counterpart Susan Rice, sources said.
The issue is again believed to have come up for discussion when Secretary of State John Kerry and Deputy Secretary of State William Burns met visiting Indian Foreign Secretary Sujatha Singh at the State Department.
However, it is not known yet, what kind of help India is providing behind the scenes for Afghanistan and the US to ink the Bilateral Security Agreement (BSA).
Responding to questions, Dobbins told Senators most of the Afghan neighbours with the exception of Iran have encouraged Karzai to sign the BSA.
"Afghanistan's regional neighbours, with the exception of Iran, also understand the importance of the BSA. I understand that President Putin of Russia, President Xi of China, Prime Minister Singh of India and Prime Minister Sharif of Pakistan have all personally urged President Karzai to conclude this agreement," Dobbins said.
He said the US is working with other Afghan neighbours in this regard.
"We are engaged with the neighbouring countries. President Karzai has just visited Iran, but he's also in I think three days from now going to be visiting India, where he'll meet with the Prime Minister and other leaders in India. He's visiting Turkey shortly thereafter," Dobbins said.
"We've already mentioned what Russia, what China, what Pakistan have said," he said.