Sixteen provisions of the 2001 law, hastily enacted in response to the 11 September 2001 attacks, are due to expire at the end of this year unless renewed by Congress.
President George Bush has repeatedly called on lawmakers to make the entire law permanent.
The act allows expanded surveillance of terrorist suspects and gives the government the ability to go to a secret court to seize the personal records of suspects from bookstores, libraries, businesses, hospitals and other organisations - the so-called "library clause".
Bills renewing the clauses due to expire were considered on Wednesday by the House Judiciary and Intelligence committees.
Meanwhile, Senate Judiciary Committee chairman Senator Arlen Specter and California Democrat Senator Diane Feinstein produced their own bipartisan version.
The three bills differed in key respects and will need to be reconciled before passage.
House Judiciary Committee chairman James Sensenbrenner introduced a bill to make the entire law permanent.
He said last week's bomb attacks in London made it even more urgent to reauthorise the legislation.
"The fact that there was a bipartisan vote...was a small step forward but there still need to be important fixes to protect civil liberties"
"The security of the American people should not be subject to arbitrary expiration dates," said Sensenbrenner, a Wisconsin Republican.
However, during Judiciary Committee debate on Wednesday, California Representative Dan Lungren suggested including 10-year "sunset provisions" to two key clauses, meaning they would need to be reauthorised by Congress once again in 2015.
That amendment was eventually adopted 26-2, with all but one Republican and one Democrat supporting it.
Sensenbrenner hopes to bring the bill to the full House for approval next week.
Democrats had pushed for even shorter time limits on the key clauses. Virginia Representative Bobby Scott offered an amendment calling for reauthorisation in 2009.
When that was defeated along party lines, New York Representative Jerrold Nadler offered another for reauthorisation in 2011. That too was defeated.
"Ten years is too long. Lots of things can happen in 10 years," Nadler said. "The liberties of Americans are worth focusing on a lot more than every 10 years."
Under the Lungren amendment, the two clauses that would not be permanent were the library clause and another dealing with so-called roving wiretaps, which allows the government to eavesdrop on suspects as they switch from phone to phone.
Previously, law enforcement agents had to get a judge's permission for each phone number they wanted to monitor.
Bush signed the original Patriot
Act after the 9/11 attacks
The House Intelligence Committee, which also has jurisdiction over the bill, approved it on Wednesday after agreeing to a five-year sunset provision on a clause that makes it easier for the government to monitor "lone wolf" suspects unaffiliated with a suspected terrorist group or country.
The Specter-Feinstein bill in the Senate would extend all three of these sections only until the end of 2009 and add several new restrictions on their use.
For example, the director or deputy director of the FBI would need to approve any orders concerning library records, book sales, firearms sales or medical records.
"This is a balanced bill. The times call for this bill," Feinstein said. American Civil Liberties Union senior counsel Lisa Graves said she was encouraged by the day's developments but the bill still needed work.
"The fact that there was a bipartisan vote not to make some key provisions permanent was a small step forward but there still need to be important fixes to protect civil liberties," she said.