Karzai and Rice said on Thursday that the much-anticipated delay was proposed by an electoral commission.
"They proposed September, and we respect whatever recommendation this commission makes," Karzai said.
Rice arrived in Kabul earlier on Thursday as part of Asia tour. A few hours after her arrival, a deadly roadside bomb exploded in the southern city of Kandahar, killing five civilians and injuring 32 others.
"The delay in the elections is because it was impossible to have it in May as we wanted it," Karzai said, blaming "technical matters".
Rice said she was informed about the delay and pledged support for the reconstruction of Afghanistan. She was in Afghanistan as part of her Asian tour that would see her return to Pakistan later on Thursday.
"I've been told by this commission that they have agreed on a date, it's September," Rice said.
Thursday's Kandahar blast may
have carried a political message
"We will stand by the Afghan people as they go through the next stage in their democratic development, the parliamentary elections that will take place this fall. We look forward to continuing to help in the reconstruction of Afghanistan."
The parliamentary vote has been put off repeatedly during the past eight months. It was originally scheduled for June 2004 alongside Afghanistan's first presidential election, but both ballots were delayed.
Thursday's bomb in the former Taliban stronghold was the deadliest bomb attack in the country since August.
Wali Allah Shahin, Aljazeera's correspondent in Kabul, reported quoting local security sources that five people were killed and 32 injured in the explosion, which took place in the central part of Kandahar.
"I've been told by this commission that they have agreed on a
date, it's September"
US Secretary of State Condoleezza Rice
Pointing to the fact that the blast occurred on a stretch of a downtown street with no military targets nearby, the sources suggested it was deliberately aimed at civilians.
Shahin said political observers believe the attack was timed to coincide with Rice's maiden visit to Afghanistan, suggesting it carried a political message even though the victims were civilians.
Officials in Kandahar said children were among the casualties, adding that those with serious injuries had been shifted to hospitals.
Rice's meeting with Karzai was set to be followed with talks with Foreign Minister Abd Allah Abd Allah, and top American diplomats and military officials later on Thursday.
Her talks were expected to focus on a number of issues, including counter-terrorism, democracy in Afghanistan and the war on drugs.
Afghanistan is Rice's third stop on a six-nation Asian trip. She arrived on Thursday in the capital Kabul from Pakistan. She is due to return later on Thursday to Islamabad for further talks with Pakistan's leadership.
Rice also visited India, and will travel to Japan, South Korea and China during the trip.
The Bush administration sees Afghanistan as a foreign-policy success after US forces ousted the Taliban and set the country on a path to its first democratic presidential elections which were held last year.