The utility said it also plans to cover the reactor building, which was hit by a huge quake and tsunami on 11 March.
Nearly 14,000 people died and another 14,000 are still unaccounted for.
Tepco unveiled its roadmap as Hillary Clinton briefly visited Tokyo to pledge America’s “steadfast support” for Japan’s reconstruction.
Radiation levels in the sea near reactor 2 rose to 6,500 times the legal limit on Friday, up from 1,100 times a day earlier, Tepco has said, raising fears of fresh radiation leaks.
Tsunehisa Katsumata, the chairman of Tepco, Asia’s largest utility, told a news conference in Tokyo on Sunday they would need up to nine months to bring the power plant to ”cold shutdown”.
He said the plan would allow the tens of thousands of families evacuated from the area around the facility to return home as soon as possible.
“We sincerely apologise for causing troubles,” Mr Katsumata said. “We are doing our utmost to prevent the crisis from further worsening.”
Japan’s government had ordered Tepco to come up with a timetable to end the crisis, now rated on a par with the world’s worst nuclear accident, the 1986 Chernobyl disaster.
But the BBC’s Roland Buerk in Tokyo says it is still not certain that the nine-month deadline can be achieved.
He says the immediate priority for Tepco is to stop radioactive water leaking into the Pacific Ocean.
The utility said it was sending remote-controlled robots into one of the reactors on Sunday to gauge radiation and temperature levels.
UK defence contractor QinetiQ said it had provided the machines, which are controlled using a standard games console.
The robots can carry out tasks such as rubble clearance, demolition and radiation testing.
Japan is a world leader in such technology, but its robots are not adapted for dirty work such as meltdowns at nuclear plants, experts say.
Emergency workers have been unable to enter any reactor building since the disaster.
Our correspondent says Japan’s recovery bill has been estimated at $300bn (£184bn) – already the most expensive disaster in history.
But the government said last week that figure might be an underestimate.
Meanwhile, US Secretary of State Clinton said in Japan she believed the country would emerge stronger from its worst crisis since World War II.
She met Prime Minister Naoto Kan and had tea with Emperor Akihito at the Imperial Palace, said to be a rare privilege for a non-head of state on a Sunday.
America has won Japanese admiration for sending scores of US ships and aircraft as well as 20,000 troops to help the relief effort.
Operation Tomodachi, or Friend, was the biggest humanitarian mission the US has conducted in Japan.
Before the quake, the two nations’ ties had been strained by a dispute over US military bases on the southern Japanese island of Okinawa.
Mr Kan’s predecessor as premier quit last year after being accused of reneging on a promise to remove at least one of the bases. – BBC