The House of Delegates gave overwhelming final approval yesterday to separate measures that would allow the giant Citicorp bank to open branches in Maryland next year and that would establish a four-year period of regional banking before the state's borders would be opened to nationwide banking.

Meanwhile, the chairman of the Senate Finance Committee delayed his panel's votes on the two bills for the third time since Friday.

Members of the House voted 133 to 0 without debate to approve the regional-interstate banking bill, which would allow banks in Maryland, 12 southeastern states and the District of Columbia to merge with or acquire banks in neighboring states until 1989. That year, states from all over the country could enter the region and compete freely with established banks.

The companion measure would apply to Citicorp, which has promised to build a multimillion-dollar credit card service center in Hagerstown if the General Assembly grants it the right to open branches in Maryland. The bill, which would let out-of-state banks open branches in Maryland before 1989 if they create 1,000 jobs and open a $25 million facility, passed on a 114-to-16 vote.

The two measures, whose passage was virtually assured in the House, now move to the Senate, where for weeks some members have sharply criticized the bills as being inconsistent.

Senate Finance Chairman Dennis F. Rasmussen (D-Baltimore) delayed a vote on the bill scheduled for Wednesday. The move was widely seen as a sign that Rasmussen, who opposes the Citicorp bill, does not have enough votes to kill it in his 11-member committee.