During Straw's trip to Iraq on Saturday, he also urged Iraqis to support the elections.
He said: "In practice, what we hope to see is a gradual phased draw-down of British troops starting, not with Basra, but with one or two of the other provinces in our area."
The phased withdrawal will start "as and when the Iraqis are satisfied that their own forces can cope completely with the responsibility. It's going to be a matter of months."
Around 8000 British troops control four of Iraq's southern provinces - Basra, Nasiriyah, Samawah and Amara.
Straw called on Iraqi politicians to accept the final results of last month's polls, saying true democrats must acknowledge it was just as easy to lose elections as to win them.
Some Sunni Arab and secular politicians say the 15 December parliamentary election was fraudulent and have demanded a re-run, although Iraq's Electoral Commission insists it was largely fair.The United Nations agrees.
Around 8000 British troops are
posted in Iraq
Straw said on Saturday: "The Iraqi people showed us that they are going to defy the people of violence and that democracy burns in the souls and hearts of Iraqi people in the same way it does in people across the world."
Preliminary results suggest the Shia United Iraqi Alliance will dominate the new parliament, although it looks unlikely it will have a majority of seats in the new parliament.
Jalal Talabani, Iraq's outgoing president, was re-selected to run for the job, the two largest Kurdish parties announced on Saturday.
The president is to be chosen by the new national parliament.
The president's re-selection was decided by leaders of Talabani's own Patriotic Union of Kurdistan (PUK) and by those of the rival Kurdistan Democratic Party (KDP) of Massud Barzani.
PUK and KDP leaders also announced they intended to merge their respective administrations within the autonomous region of Kurdistan, bringing all three of their provinces under single rule.
Talabani (L) predicts a new govern-
ment will be formed in weeks
Talabani predicted on Saturday that a new government could be formed within weeks.
Meeting with Straw in Baghdad, Talabani said that Shia, Sunni Arab and Kurdish political groups had agreed in principle on a national unity government that could be formed within a few weeks.
Western diplomats in Baghdad have speculated that a government could be in place by the second half of February.
Talabani said: "In principle we are agreed to have a national unity government. Everyone is expecting to have it as soon as possible, but you know the devil is in the details. For that we hope that we will be able to solve it as soon as possible. I'm expecting some weeks."
Sunni politicians have warned that anger at results they say are forged could prompt more attacks, not just by al-Qaida-linked fighters, bent on wrecking the US-led political process, but also by Sunni groups that backed the vote.
Those warnings have been followed by a spate of bombings across the country that have killed scores of Iraqis, both Shia and Sunnis.
"In democracy, it is important to understand that you can lose elections as well as win them"
British foreign secretary
At a news conference, Straw said: "As with any complicated election there are complaints about the elections. There are proper processes for these to be investigated. In democracy, it is important to understand that you can lose elections as well as win them."
He said he and Ibrahim al-Jaafari, Iraq's prime minister, discussed the need for improved co-ordination between Iraqi and US-led security forces.
Al-Jaafari said the government would introduce a new security plan to combat the surge in fighting over the next few days. He gave no details.
Meanwhile, a US woman journalist was kidnapped by armed men in the Iraqi capital on Saturday and her translator killed. She was the latest Westerner to be held in the war-torn country.
Elizabeth Colton, a US embassy spokeswoman, said: "An American journalist is missing. We are investigating."
Iraqi security officials said a US woman journalist was abducted by armed men in the Adl district of western Baghdad and that her translator had died.
The journalist was scheduled to
meet Adnan al-Dulaimi (L)
An Iraqi defence ministry official said the interpreter was able to tell soldiers before he died that the journalist was kidnapped.
Officials said the unnamed reporter was seized on her way to interview prominent Sunni Arab politician Adnan al-Dulaimi.
Baghdad violence on Saturday left 15 people wounded, including six policemen, when a bomber drove a booby-trapped car at a police commando convoy in Baghdad.
Press watchdog Reporters sans Frontieres (Reporters without Borders, RSF) expressed alarm at the kidnapping and shooting.
RSF said it was particularly "appalled by the news that the interpreter, Alin Ghazi Jack, an Iraqi Christian, was shot dead by her abductors.
"Journalists working in Iraq have once again been caught in a deadly ambush," the Paris-based press freedom organisation said. "The interpreter’s death confirms that the Iraqi press continues to be the chief victim of the infernal climate for the media in this country.