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Northern Ireland police extended the detention of Adams by another two days on Friday (local time) to give detectives more time to question him about a 1972 murder, raising the stakes in a case that has rocked the British province.
Sinn Fein, which shares power in Northern Ireland and has gained popularity south of the border during the country's financial crisis, could win as many European Parliament seats as Prime Minister Enda Kenny's Fine Gael party in the May 23 poll, according to a survey in the Sunday Business Post newspaper.
The party's candidates lie third in the two four-seat rural constituencies and its Dublin contender is second, although Ireland's proportional representation voting system favours larger parties who run more than one candidate because running mates can pick up surplus votes from those elected.
Sinn Fein, which is the second largest opposition party in Dublin's parliament after Fianna Fail, failed to win a seat in the last European elections five years ago after capturing its first ever seat in the European parliament in 2004.
It was the second opinion poll in a week which has shown Sinn Fein are poised to perform well in the elections that will take place the same day as local polls.
However, the 500 potential voters surveyed in each constituency were interviewed between Monday and Thursday of last week, mostly before the arrest of Adams on Wednesday.
Northern Ireland Deputy First Minister Martin McGuinness, a Sinn Fein member, reiterated on Saturday that the arrest was "inextricably linked" to the polls when he addressed hundreds of supporters who staged a rally by a new mural of Adams painted in Belfast.
Sinn Fein will also contest European and local elections in Northern Ireland.
Adams' arrest over the killing of Jean McConville is among the most significant in Northern Ireland since a 1998 peace deal ended decades of tit-for-tat killings between Irish Catholic nationalists and mostly Protestant pro-British loyalists.
The Sinn Fein leader, who is a member of parliament in the Irish republic, has been dogged throughout his career by accusations from former IRA fighters that he was involved in its campaign of killings, a charge he has repeatedly denied.
When he was arrested, Adams said that he was "innocent of any part" in the killing, which he said was "wrong and a grievous injustice to her and her family".