An Afghan cabinet minister who asked not to be named told media on September 6 that the trip was delayed "by the U.S. government because of Mr. Ghani's opposition" to the text of a draft peace agreement between the United States and the Taliban.
Tolo News quoted sources familiar with Ghani's planned trip as also saying the visit had been postponed.
The report said the president was originally due to travel to Washington on September 7 with a delegation for talks with his U.S. counterpart, Donald Trump, on September 9.
The development emerged after the U.S. envoy negotiating with the Taliban, Zalmay Khalilzad, briefed Afghan officials in Kabul on an agreement "in principle" the two sides had reached following nine rounds of talks in Qatar.
On September 5, reports said Khalilzad abruptly returned to the Qatari capital, Doha, for more talks with the militant group.
The Taliban has so far rejected negotiations with the Afghan government, seeing it as a puppet of the United States.
While U.S. and Taliban negotiators appeared to be closing in on an accord to end the fighting, the militant group has been stepping up operations across Afghanistan in recent days.
Early on September 6, the Taliban launched an offensive against the western Afghan city of Farah -- the third provincial capital to come under attack in less than a week.
The militant fighters briefly seized an Afghan Army recruitment center in the capital of Farah Province, officials say.
With U.S. support, Afghan forces pushed the attackers back a few hours later, local police spokesman Mohibullah Mohib said, adding that fighting was continuing on the outskirts of the city.
Ghulam Mohddin Khairkhah, Farah's provincial security chief, told media that the fighting around the city was sporadic.
Ten Taliban militants were killed in the fighting, along with one paramilitary Afghan police officer, according to Mohib.
Provincial Governor Mohammad Shoaib Sabet said that at least two civilians were killed and another 15 people were wounded in the attack.
Air strikes were carried out against the militant group, Sabet said.
"We continue to support [Afghan forces] as they thwart the Taliban's attack on Farah," said U.S. Army Colonel Sonny Leggett, a spokesman for U.S. Forces-Afghanistan.
Taliban spokesman Qari Yousuf Ahmadi earlier said a "massive operation" was under way.
Farah Province, which borders Iran, has been the scene of intense fighting in recent years. In May 2018, the Taliban made a major attempt to capture Farah city but were eventually driven back by Afghan and U.S. forces.
The Taliban assault comes after the militants on August 31 attempted to seize the provincial capital of Kunduz in the north and sporadic fighting continued on the outskirts all week.
The following day, they launched an operation in the city of Pul-e Khumri, the capital of neighboring Baghlan Province.
Meanwhile, the national capital, Kabul, was rocked by two major bombings this week that have claimed dozens of lives.