At least 14 people were killed and over 30 wounded when a motorcycle laden with explosives blew up during a campaign rally in Rustaq, north Afghanistan, on Saturday.
But under pressure to break the impasse with the group, Washington appeared to change tack in June when US Secretary of State Mike Pompeo said his country was prepared to "participate" in talks.
Khalilzad flew to Kabul on Saturday to meet with the Afghan president, Ashraf Ghani.
Khalilzad, a former US ambassador to Iraq and to the United Nations and who was born in Afghanistan, is on his first trip to the region since being appointed by the State Department last month as special representative for Afghan reconciliation.
Khalilzad's trip started out from Afghanistan.
There was no confirmation of the talks from the U.S., although a top Afghan government official told The National it was an "initial meeting to discuss peace" while refusing to disclose details.
Continued fighting has raised questions about the viability of the USA strategy to end the war, which for the past year has focused on forcing the militants to the negotiating table, largely via more air strikes.
They have ramped up attacks in strategic provinces and have also directed Afghans to boycott the parliamentary elections.
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Scores of people had gathered to listen to the candidate, but police said she was not at the rally at the time of the blast. He said the bomb was planted near the house where the wedding was taken place and targeted the participants of the wedding.
Officials also report at least 11 soldiers were captured.
No one immediately claimed responsibility for the attack but Taliban insurgents are active in the province.
Since then, the US president announced an Afghan strategy that called on Pakistan to do more to push the Taliban to the negotiating table and to end safe havens for insurgents, an allegation Islamabad denies.
There are 2,565 candidates vying for seats in the 249-member chamber, including 417 women candidates.
The two officials discussed ways of achieving peace and stability in Afghanistan and Qatar's role in the peace process in the country, The Peninsula Qatar reported.
"Our fighters have killed the police chief and 25 Afghan soldiers in two provinces on Saturday night", its spokesman, Zabiullah Mujahidhe, said in a statement.
The violence has been on the rise as Afghan security forces struggle against a surge in attacks by militants as the country is preparing for parliamentary elections slated for October 20.