NEW DELHI, FEB. 19 -- Terrorist bombs went off in or near four district courts across Punjab today, reportedly killing 13 persons and injuring nearly 50 as the violence in the predominantly Sikh state took an ominous turn.

The shooting deaths of three other persons brought the toll to 16 over 24 hours and to more than 230, by conservative count, since the first of January. If it continues, it is a pace that would clearly surpass the official toll of 1,230 deaths for last year. The official toll for 1986 was 640, a demonstration of the escalating level of violence in the strategic north Indian state.

News agencies said police in the state capital, Chandigarh, blamed the Khalistan Commando Force, a group that demands that Punjab be made an independent Sikh state, to be called Khalistan.

{Suspected Sikh extremists killed 11 members of a Sikh family Saturday near Amritsar, the Sikh holy city, and set their bodies on fire, Reuters reported, quoting police.}

While the violence this year has intensified dramatically, it has received relatively little attention in the Indian press. With the state under the control of the central goverment for the past several months, New Delhi has not been eager to call attention to the trouble.

Today's bombings brought a quick response, however. The central government immediately ordered a statewide alert and police officials in the capital issued a warning that there could be bombings in New Delhi as well.

While there were no claims of responsibility for today's apparently coordinated bombing, there was little doubt that they were the work of Sikh militants.

The militants have used small, relatively simple bombs in past incidents; few were as powerful as those that went off at the court compounds today.

Courts in Indian cities usually consist of a series of one-story buildings in a large compound that includes lawyers' desks, clerks to help the illiterate, tea stalls and other facilities. Hundreds of people usually are in the compound during working hours.

Over the past year, police have claimed regularly that they had broken the back of the militants' activities. Officials point to the killing of 259 suspected terrorists and the arrest of 2,513 since the imposition of rule from New Delhi last year.

But each claim of police success seems to spark a new phase of violent tactics seemingly designed both to frustrate the government and to demonstrate the continued power of the militants to disrupt life.

At different times in recent years, the militants have conducted massacres of bus passengers, , high-visibility attacks in New Delhi and campaigns to drive Hindu traders out of Punjab State.

Officials and residents of Punjab say, however, that the majority of the deaths result from attacks on individuals and families, many of them Sikhs whom the militants accuse of being too close to the government.

Today's explosions occurred at the district courts of Amritsar, Gurdaspur, Hoshiarpur and Patiala. A bomb also was found in a container hung on a bicycle at the district courts complex in Jullundur this afternoon and Army bomb disposal experts were rushed to the site.