* Boycott increases chances of Islamists sweeping poll
* Opposition aims to erode legitimacy of vote (Adds Mursi quotes)
By Yasmine Saleh and Tom Perry
CAIRO, Feb 26 (Reuters) - An alliance of Egyptian opposition parties decided on Tuesday to boycott parliamentary elections in protest at an election law they say favours the Muslim Brotherhood, increasing the chance that Islamists will sweep the vote.
The boycott by liberal and leftist parties opposed to President Mohamed Mursi aims to undermine the legitimacy of the vote and shows the polarisation that has defined Egyptian politics since Hosni Mubarak was toppled two years ago.
It raises the prospect of an election fought mostly between Mursi's Muslim Brotherhood and more hardline Islamist groups such as the Salafi Nour Party. The vote is to be held in four stages between late April and June.
The National Salvation Front (NSF) - an array of liberal and leftist parties struggling to compete with the Islamists - said there should be no elections for the lower house of parliament without a law guaranteeing fair polls.
The law was passed this month by the Islamist-dominated upper house of parliament, which has been exercising legislative power in the absence of a lower house. The Islamists deny opposition accusations that the law divides constituencies in a way that favours the Muslim Brotherhood.
"There can be no elections without a law that guarantees the fairness of the election process and a government that can implement such a law and be trusted by the people," said Sameh Ashour, a spokesman for the NSF, who also called for "real independence of the judiciary".
With deep grass roots networks, the Islamists have won all elections since Mubarak was swept from power in a popular uprising that for a while brought Egyptians together in a display of unity rarely seen since then.
Divisions between the Islamists and their opponents have widened since Mursi won last year's presidential election. Tensions spilt into lethal street violence late last year when the president was accused of staging a power grab - accusations the Islamists dismissed as propaganda.
Seeking to convince the opposition to take part, Mursi invited them to talks on Tuesday to address concerns about the vote, but the alliance declined to attend. "We tell President Mursi: talk with yourself and your party," Ashour said.
Mursi went ahead with the talks anyway. "I hope these elections will be fully fair," he told the televised meeting attended by Islamists, smaller parties and independents. "We all bear the responsibility and I bear the most responsibility."
Mursi said he hoped "our dear brothers who did not meet us today" would join the talks at a later date.
If the past is anything to go by, Mursi and the Brotherhood will press on regardless. In December, he held a referendum on a constitution opposed by the opposition, securing its approval and signing it into law despite fierce protest.
"The call for boycott indicates the lack of trust the opposition has in the Brotherhood government and may also speak to their own capacities to effectively compete should they run," said Elijah Zarwan, a Cairo-based political analyst.
The boycott means parties led by some of the most prominent non-Islamist politicians will sit out the vote.
These include the Popular Current led by Hamdeen Sabahy, a leftist who came third in the presidential election won by Mursi last June, and the Dustour Party led by Mohamed ElBaradei, a former U.N. nuclear agency chief.
"This is to protest against the elections law that we did not participate in drafting, and about which our opinion was not taken," said Heba Yassin, a spokeswoman for Popular Current. "We reject the continuation of Mursi's oppressive policies that have led to nothing but more bloodshed and political problems."
The lower house was dissolved last year after a court ruled that the previous election law used to elect it was illegal.
The Muslim Brotherhood's Freedom and Justice Party won about 40 percent of seats in the old lower house, with the Nour Party in second place. The Nour Party announced this week that it would take part in the elections.
Hassan Nafaa, a political scientist and a critic of the Muslim Brotherhood, said the boycott would undermine the legitimacy of the election. But he also foresaw some parties eventually breaking the boycott.
"If one of the front parties decided to enter the elections at a later stage, this will be a major blow," he said.
Police arrested 55 people on Tuesday during a failed attempt to re-open Tahrir Square which has been occupied by anti-Mursi demonstrators since November, a security source said.
State media described the police operation as a "peaceful process" that prompted a violent reaction from street venders who threw petrol bombs. Police removed barbed wire barricades, briefly opening the square to traffic, but they were swiftly re-erected by the youths that man them, the source said. (Writing by Tom Perry; Editing by David Stamp and Robin Pomeroy)