WASHINGTON — Mayor Giuliani’s political problems are mounting, as a lesser-known Republican rival, Mitt Romney, has surged in recent polls and a drug company with ties to his consulting firm has pleaded guilty to misleading the public about the potent painkiller OxyContin.

The former mayor has been ahead of Mr. Romney and Senator McCain of Arizona for months, but polls in the last two weeks have the former Massachusetts governor gaining or leading in New Hampshire, the site of the first primary, and in Michigan. Though Mr. Romney remains far behind Mr. Giuliani in national surveys, the bump in the Granite State is a sign his campaign may be catching on with Republican primary voters.

Mr. Romney, who served one term in the Massachusetts statehouse, has had to work much harder than Messrs. Giuliani or McCain to introduce himself to voters. He has received a flurry of publicity since what was widely considered a strong performance in the first Republican presidential debate last week. He has garnered headlines over a spat about his Mormon faith with the Reverend Al Sharpton, and he is set to be featured this weekend on the cover of Time magazine and on “60 Minutes.”

For Mr. Giuliani, it has been a week of missteps and negative stories, the latest coming yesterday as the drug manufacturer Purdue Pharma and its top executives pleaded guilty to a felony charge of misbranding OxyContin, the prescription pain relief medication that federal prosecutors said has resulted in “scores” of deaths from abuse. Mr. Giuliani’s private firm, Giuliani Partners, is a consultant for Purdue Pharma and has tried to help the company weather the OxyContin controversy for the past five years.

Under a settlement with the Justice Department, Purdue and its president, chief legal officer, and former chief medical officer will pay more than $630 million in penalties and fines. They admitted to falsely claiming that OxyContin was less addictive, less subject to abuse, and less likely to cause withdrawal symptoms than other pain medications.

Neither Mr. Giuliani nor his firm were named or implicated in the settlement, and their relationship with Purdue began in 2002, after the crimes occurred. Giuliani Partners, which remains a consultant to the company, declined to comment through a spokeswoman, Sunny Mindel.

Still, the settlement adds to the cloud that has surrounded some of Mr. Giuliani’s personal dealings, particularly through his association with his now disgraced former police commissioner, Bernard Kerik. It was Kerik who took charge of advising Purdue on security, according to a Giuliani Partners press release from 2002. Kerik last year pleaded guilty to illegally accepting gifts while he headed the city’s Department of Correction, and he is currently under federal investigation for tax evasion, conspiring to eavesdrop, and making false statements.

Mr. Giuliani and Kerik met with the head of the Drug Enforcement Agency, Asa Hutchinson, on behalf of Purdue in 2002, while the company was under investigation, the New York Times reported in 2004.

In a telephone interview yesterday, Mr. Hutchinson said the former mayor’s dealings with him did not relate to the crimes involved in the plea deal, but to a separate “administrative investigation” of one of Purdue’s plants.

“I saw nothing inappropriate about it,” Mr. Hutchinson said of Mr. Giuliani’s request for a meeting. He described it as “routine,” saying Mr. Giuliani’s role was to advocate for the company.

“He was doing his job,” he said. “Rudy did his job, and the DEA did its job.”

Mr. Giuliani’s presidential campaign has also come under strain this week as he has publicly grappled with his position on abortion. His aides yesterday backed off a report in the Times that he would step up his support for abortion rights while bucking the traditional route of focusing on the earliest primary states — Iowa, New Hampshire, and South Carolina — in favor of larger states such as New York, California, and Florida, which have more moderate Republicans and are moving up their elections. A spokeswoman, Maria Comella, said portions of the Times article were “widely overstated.”

“We’re committed to playing in Iowa, New Hampshire, and South Carolina,” she said.

Mr. Giuliani is expected to address the abortion issue on Friday in an appearance at Houston Baptist University, as well as in an interview on a Sunday morning talk show.

His struggles could be helping Mr. Romney, who has acknowledged switching his position and now opposes abortion rights. In a speech last night to the Massachusetts Citizens for Life, he said his earlier position was “wrong,” and he assailed abortion, gay marriage, and stem cell research.
Mr. Romney shot past Messrs. Giuliani and McCain in New Hampshire this week, garnering 32% of likely primary voters in a Survey USA/WBZ poll released Tuesday. In January, he had placed third with 21%. Mr. Romney also gained in a New Hampshire poll released April 30 by the American Research Group. While Mr. McCain led with 29%, Mr. Romney received 24%, up seven percentage points from a similar poll in March.

In an American Research Group survey of likely Republican voters in Michigan, Mr. Romney led with 24%, a 16-point boost from his standing in February.

He has raised more money than his competitors and is the only candidate to have run advertisements. Mr. Romney also enjoys better name recognition in Michigan, where his father was a former governor, and in New Hampshire, which is adjacent to his home state.

“The more that voters get to either hear or see Governor Romney and learn about his ideas and his platform, the more progress we make and the bigger our organizational support grows,” a campaign spokesman, Kevin Madden, said.