NEW DELHI - India's federal police have arrested a senior official of state-run Punjab National Bank (PNB), the agency said on Wednesday, as an inquiry into a $1.8-billion fraud at the bank expands a week after it unveiled the size of the alleged scam.

India's federal police, the Central Bureau of Investigation (CBI), said Rajesh Jindal, the former head of the bank's Brady House branch in Mumbai between August 2009 and May 2011, was arrested, taking to six the tally of bank officials arrested.

The branch is at the center of the alleged fraud involving firms tied to diamond merchants Nirav Modi, whose lawyer has denied any wrongdoing, and his uncle, Mehul Choksi, whose firm, Gitanjali Gems, has said it has nothing to do with the case.

The bank has alleged that as far back as 2011, firms tied to the duo began receiving fraudulent letters of undertaking (LOUs) from its Brady House branch that enabled them to borrow money from overseas banks.

"During his tenure at PNB Brady House branch, the practice of issuance of LOUs without sanctioned limits to Nirav Modi group firms had started," a CBI spokesman said, referring to Jindal.

Jindal, now posted as a general manager handling credit at the bank's head office in New Delhi, is the highest profile bank official so far arrested, said a second CBI officer, who declined to be identified.

It was not immediately possible for Reuters to reach Jindal, who is in custody and expected to appear in court on Wednesday.

Punjab National Bank has not commented on the arrests since it triggered the inquiry with a complaint to federal police that two of its employees had been issuing fraudulent letters of guarantees to firms led by Modi and Choksi.

Late on Tuesday, the CBI said it had also arrested five officials from the groups of Nirav Modi and Mehul Choksi.

Both groups have not commented on the latest arrests.

Shares in PNB, which have lost more than a quarter of their market value since the scandal became public, were up 1 percent in early trading on Wednesday.

(Reporting by Aditya Kalra; Writing by Swati Bhat and Euan Rocha; Editing by Clarence Fernandez) ((euan.rocha@tr.com; +91 22 6180 7257; Reuters Messaging: euan.rocha.reuters.com@reuters.net))