"The United States stands ready to assist in any way we can an Afghan-led reconciliation process to find a peaceful end to this conflict," he said in a statement.
"I look forward to calling on President Karzai and discussing next steps."
Grossman's visit comes in the wake of an announcement by the Taliban that it planned to open a political office in Qatar ahead of talks with Washington on ending Afghanistan's 10-year war.
Secretary of State Hillary Clinton despatched Grossman to Kabul to discuss the development with Karzai, who was reportedly concerned that he would be sidelined in the Qatar talks.
Washington has consistently said that any talks with the Taliban to end the war could only take place with the agreement of the Afghan government, which eventually should lead the process.
"I have made it clear to President Karzai that we will work with him, under his leadership," Clinton said.
A US official said that if Karzai was agreeable, the talks could open within weeks.
Grossman's visit comes a day after French President Nicolas Sarkozy said he was considering an early exit from Afghanistan after an Afghan soldier shot dead four unarmed French troops during a sports session inside a base.
France has some 3,600 troops in Afghanistan with US-led coalition forces totalling about 130,000. The coalition forces plan to pull out their combat troops by the end of 2014.
Grossman had planned to visit neighbouring Pakistan ahead of his trip to Kabul but was snubbed by Islamabad amid a drastic deterioration of ties, particularly after a NATO air strike near the Afghan border on November 26 killed 24 Pakistani troops.
US officials have deep concerns about the role of Pakistan, with many believing its intelligence services maintain ties with the hardline Taliban militants inside Afghanistan.
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