(Reuters) -Italian lender BPER has increased its bid for smaller rival Popolare di Sondrio to 5.44 billion euros ($6.39 billion), the bank said on Thursday, heating up the race in the country's financial sector that has seen a flurry of deals and offers.

The bid represents a premium of 3% based on Popolare di Sondrio (BPSO) shares' last closing price, valuing the bank at 5.44 billion euros, according to Reuters' calculation.

The revised offer includes 1.450 newly issued BPER shares and an additional cash consideration of 1.00 euro per BP Sondrio share.

The bid comes just a day after Italy's antitrust authority, AGCM, conditionally approved BPER's deal for BPSO, stating that BPER is required to sell six branches, which includes 5 of BPER and 1 of BP Sondrio, within 10 months.

BPER and BPSO have in common their main shareholder, insurer Unipol, which distributes its products through both banks. Unipol agreed to BPER's bid last week.

In February, BPER joined in a raft of takeover bids rocking the country's financial sector, with an initial offer of 4.3 billion euros for all BPSO shares.

BPER's market capitalisation of about 10.9 billion euros is more than double mid-sized lender BPSO's market value of 5.32 billion euros, according to LSEG data.

The increased offer from Italy's fourth-largest bank comes just weeks after BPER Chief Executive Gianni Franco Papa said that the bank would stick to its current bid.

Italy's banking sector has in the last year witnessed a wave of bids and offers, including UniCredit's all-share offer for smaller peer Banco BPM , creating a complex web of deals between some of its biggest players.

($1 = 0.8511 euros)

(Reporting by Gursimran Kaur in Bengaluru; Editing by Alan Barona and Maju Samuel)