NEW DELHI.-For the first time since serious fighting broke out in East Pakistan late last week, substantial numbers of refugees were reported today to be crossing the border into Indian territory.

Indian press agency reporters stationed along the border said hundreds of families mostly women and children had crossed the Ganges River from Rajshahi, where West Pakistani troops were reported to have moved through the town against East Pakistani adversaries .

At other points along the border, people who had first fled from towns to neighboring villages crossed over, saying they had feared that West Pakistani planes would bomb their rural sanctuaries next.

As usual, there were conflicting reports of the situation in East Pakistan. While the West Pakistani radio asserted that the situation in cities and towns remained "calm," East Pakistanis at the border reported heavy fighting in several towns.

In general, however, it appears that West Pakistani troops are beginning to have difficulty maintaining their resupply system and that the East Pakistanis, while disorganized are beginning to mount stiffer guerrilla resistance as West Pakistani troops attempt to spread their control from cities to district towns.

Except for the first-hand accounts of a few Western newsmen who have ventured into East Pakistan on short trips with the help of the "liberation forces" of East Pakistan, most reports reaching here are considered highly questionable. Most come from Indian reporters in West Bengal strongly sympathetic to the East Pakistani bid for independence. They have repeatedly reported great victories for the resistance forces.