Some council members grumbled when Bolton made the request saying they were too busy for the daily briefings.
Bolton said: "Sweet reason prevailed and today the council agreed to try it as an experiment."
The new daily briefings agreed on Friday are due to begin next Tuesday, when Haiti holds presidential elections, and will regularly cover "hot spots and crises and overnight events around the world," Bolton said.
But at the insistence of Wang Guangya, the Chinese ambassador, the experiment was limited to an initial two-week period, council diplomats said.
The Bush administration sent Bolton to New York to shake things up at the United Nations following findings of mismanagement and corruption in the $64 billion oil-for-food programme for Iraq and a brewing scandal in UN procurement.
But some ambassadors were clearly not thrilled when Bolton decided to bring the UN reform campaign to the 15-nation Security Council, the pre-eminent UN body on matters of international peace and security.
He timed his initiative to Washington's assumption of the council's rotating presidency for the month of February.
At the first meeting of Washington's presidency on Thursday, he announced he was trying to instill a new sense of "intellectual discipline" in the council, by holding daily briefings and by insisting on starting meetings on time.
Bolton is trying to encourage
punctuality at the council
But by 10am Bolton was the only ambassador in the council chamber.
A day later, however, ambassadors appeared to show greater inspiration. Wang and Jean-Marc de la Sabliere, the French ambassador, arrived promptly into the chamber as the council chimes marked the hour.
But sentiment was still not unanimous. Adamantios Vassilakis, the Greek ambassador, said: "Do you see me running?" as he strolled by reporters.
At a second council meeting a few hours later, on-time performance was already flagging again, diplomats said.