* Italian bonds drop after Renzi election remarks raise concerns

* Pound pressured as latest polls show ruling party lead narrows

* U.S., UK markets were closed for holidays on Monday

TOKYO, May 30 (Reuters) - The dollar firmed on Tuesday, taking back ground against the euro and sterling which were pressured by political uncertainties in the UK and eurozone.

The dollar index, which tracks the greenback against a basket of six rival currencies, rose 0.3 percent to 97.706 , pulling further away from a 6-1/2-month low of 96.797 plumbed last week.

U.S. and UK markets were closed for holidays on Monday, giving investors fewer directional clues to follow.

British Prime Minister Theresa May's lead over the opposition Labour Party dropped to 6 percentage points in a poll published on Tuesday, the latest to show a shrinking lead for the ruling Conservatives ahead of June 8 elections since the Manchester terrorist attack.

Sterling slipped 0.2 percent to $1.2812, moving back toward a three-week low of $1.2775 touched on Friday.

The euro was also on the defensive after former Italian Prime Minister Matteo Renzi said on Sunday that it makes sense "from a European perspective" for Italy's next election be held at the same time as Germany's, scheduled for September. His comments led to a selloff in Italian government debt on Monday.

"The euro is under downward pressure following Renzi's comment that he would favour snap elections," as well as proportional representation that could lead to a hung parliament, said Masafumi Yamamoto, chief forex strategist at Mizuho Securities.

"It seems the market has begun to realize there's political uncertainty in Italy," he said. "The dollar/yen, meanwhile, is waiting for clarification on balance sheet reduction by the Fed."

Markets are mostly pricing in the possibility that the U.S. central bank will hike interest rates by a quarter point to 1.00-1.25 percent at its June 13-14 policy meeting, with attention turning to clues on the timing of when the Federal Reserve intends to begin paring its $4.5 trillion balance sheet.

The dollar edged down 0.1 percent against its Japanese counterpart to 111.17 yen, but remained solidly mired in its recent narrow range between last week's high of 112.13 and May 18's low of 110.24.

The euro slipped 0.3 percent to 123.82 yen after drifting as low as 123.71, its weakest since May 19.

(Reporting by Tokyo markets team; Editing by Shri Navaratnam)