VIENNA, JAN. 1 -- Albanian Communist leader Ramiz Alia pledged in a New Year's message that the nation's first democratic election in February will be "completely free," the state ATA news agency reported today.

In a separate dispatch, the agency said the government had decided to permit people not related to each other to join in running private businesses. The move expanded on a decree issued in July that permitted small-scale private business for the first time in decades of Communist rule but restricted the operations to members of one family.

Despite the pledges of democracy and economic reform, refugees continued to flee the country. Albanians by the thousands have flooded into Greece in recent days after trekking over isolated mountain passes joining the two countries.

An estimate of the refugee total was not available, but a Greek police official in Filiates, near the border, said today that more than 3,500 Albanians arrived overnight. Refugees said that Albanian border guards had allowed them to pass freely, but the Albanian government denied that the border had been opened.

Greek officials expressed fears tthat they would be overwhelmed by the influx, and Premier Constantine Mitsotakis held an emergency meeting on the situation with his foreign and interior ministers and military chief of staff. Mitsotakis said he would dispatch senior officials and relief crews to the Albanian border to coordinate aid to the refugees.

Alia's New Year's message reiterated the leadership's commitment to democratic elections but gave no sign of heeding opposition calls for a later date. "Elections to the new People's Assembly will be conducted on Feb. 10," ATA quoted him as saying. "These elections will be completely free and democratic, pluralist and secret."