He said the U.S. is working hard toward a lasting and honorable peace agreement and a sovereign Afghanistan which poses no threat to any other country.
Some in Afghanistan saw it as a response to President Ashraf Ghani, who on Sunday declared that "Our future can not be decided outside, whether in the capital cities of our friends, nemeses or neighbors".
Such an accord would be followed by intra-Afghan peace negotiations on a political settlement and a permanent cease-fire.
Ghani emphasied that peace was only possible "between the Islamic Republic of Afghanistan and the Taliban movement".
The talks, held in Qatar since late previous year between the Taliban and USA officials, have brought hopes for an agreement allowing U.S. troops to leave in exchange for a Taliban promise that Afghanistan will not be used by militants as a base from which to plot attacks overseas.
The U.S. envoy for Afghan peace Zalmay Khalilzad has expressed hopes that this will be the last Eid where Afghanistan is at war.
The Taliban have refused to negotiate with the Afghan government, dismissing it as a US puppet, and on Tuesday they declared the September 28 election a "sham".
Few details have emerged, but Mr. Khalilzad and the lead Taliban negotiator, Mullah Abdul Ghani Baradar, have been traveling in recent days to brief several countries involved in the process on the latest developments.
Washington has said it wants a peace deal finalized by September 1, and some US officials have hinted at the possibility that the Afghan presidential election set for September 28 could be canceled in the event of a peace settlement and the formation of an interim government that the Taliban would join. The attack killed 14 people and wounded 145, a lot of them civilians.
The Taliban do not recognise the Kabul government and have refused to talk to it.
The Taliban have denounced the election as a sham and threatened to attack rallies.
Last week, the Taliban announced the start of their annual spring offensive, dismissing an offer of peace talks by President Ashraf Ghani. The militants, fighting to restore their version of strict Islamic law to Afghanistan, said their campaign was a response to a more aggressive United States military strategy adopted previous year, which aims to force the militants into peace talks.
The US has been negotiating with its longtime foe over the past year for a pact that would see the Pentagon begin to withdraw its 14,000 troops from Afghanistan. The some 20,000 American and allied troops that remain are carrying out airstrikes on the Taliban and IS militants, and are working to train and build the Afghan military.
Residents of different provinces called on the Taliban to quit violence and celebrate Eid together with other Afghans in a peaceful environment. In September 2016, the Afghan government signed a deal with Hekmatyar in the hope that other warlords and militant groups would seek better ties with Kabul. Rampant corruption in the Afghan government and a long tug-of-war within the US-brokered national unity government has had a negative impact on the government's efforts to eradicate terrorism.