As the toll in Monday's two bombing attacks on opposite sides of Ireland rose to 23 dead and several others critically injured, British and Irish security forces today sought to stop the escalating attacks on British soldiers and officials by Irish Republican Army terrorists.

Troops and police on both sides of the border between Ireland and British Northern Ireland conducted a massive manhunt for the terrorists whose bombs murdered Lord Mountbatten and three other people in his fishing boat just off the northwestern coast of Ireland and, five hours later, killed 18 British soldiers near the eastern coast of Northern Ireland. A British tourist also died when surviving soldiers returned the fire of terrorist snipers.

Today, in what was feared here to be a related attack, another bomb blew up an outdoor stage in the central square of Brussels, injuring 15 people, including four members of a British army band, just before the band was to perform there during the Belgian capital's millenium celebration.

Prime Minister Margaret Thatcher met with members of her Cabinet here today, and her Northern Ireland secretary, Humphrey Atkins, conferred with army and police commanders in Ulster. They discussed possible new steps to counter the upsurge of sophisticated IRA bomb and gun attacks that this year have killed 30 British soldiers, a number of Ulster police, prison and reserve officers, a British ambassador, a senior member of Parliament and Lord Montbatten, a war hero and senior statesman of Britain's royal family.

Britain has become somewhat anesthetized to Ulster violence -- nearly 2,000 people, including 319 British soldiers, have died since British troops were sent there 10 years ago. But the magnitude of Monday's killings and the assassination of Lord Mountbatten, a celebrated military commander and diplomat and beloved patriarch of the royal family, appeared to have left the country in shock.

Political reaction was muted by the summer parliamentary recess and the absence of many Britons on vacations abroad. Next Wednesday, after the vacation season has ended, Mountbatten's funeral in Westminster Abbey will be attended by royalty, government leaders and military officers from throughout the world, and may serve as a focus for the nation's grief.

The IRA said in its statement Monday that Mountbatten was a "symbolic" target selected for his importance to "sentimental" Britain.

Monday's violence clearly was intended to dramatize the IRA'S dissatisfaction with 10 years of British military occupation of Ulster. Two weeks ago, on the mid-August anniversary of the arrival of British troops in Northern Ireland in 1969, British soldiers found in an abandoned rural house, and safely dismantled, a massive bomb and its remote control detonator that could have been used to blow up a passing truckload of soldiers the same way that a bomb did on Monday.

Monday's big bombs were detonated by remote control by members of the Provisional IRA paramilitary wing, according to its own detailed statements, teletyped to British and Irish news organizations. A rival IRA faction, the Irish National Liberation Army, murdered senior Conservative member of parliament Airey Neave March 30 with a car bomb exploded by a sophiscated two-step mercury device as he drove up the ramp of the House of Commons underground garage here.

Other soldiers and security officers have been killed by both kinds of bombs in Ulster and by snipers shooting from moving vehicles and from homes and shops commandeered from innocent Ulster families.

Britain's ambassador to the Netherlands was assassinated by suspected IRA gunmen just outside his residence in The Hague March 22. The next day NATO, was similarly shot and killed in front of his Brussels home.

Today's explosion in the center of Brussels followed a July 5 bombing that seriously damaged the British consulate in Antwerp. The visiting band of the Duke of Edinburgh's royal regiment was just moving from its bus to the temporary bandstand in the medieval central square of 1,000-year-old Brussels when a bomb hidden under the stage exploded shortly before 3 p.m. today. None of the injuries was believed to be serious.

British security officials are worried about the deadly efficiency of these attacks, their wide geographical spread and the fact that not one terrorist involved in any of this year's killings has been caught or killed by police or the 13,000 British troops in Northern Ireland. There were renewed calls today from British legislators and newspapers for stepped-up security measures, restoration of the death penalty for terrorist killings and increased cooperation by the Republic of Ireland in catching, convicting and imprisoning IRA terrorists who flee there after bombings and shootings just across the border in Ulster.

This is a sore point in British-Irish relations. The British army and Ulster police see the 300-mile, unmarked border with relatively few checkpoints as offering sanctuary to hit-and-run terrorists. British soldiers and police officers are not allowed to pursue suspects across the border and Ireland has refused to sign an extradition treaty that would force its courts to send terrorists caught there back into Britain for trial.

Irish officials point to their country's tough anti-terrorism law that authorizes the arrest of anyone a police officer suspects of being a terrorist and the 150 convicted IRA terrorists now in prisons there. They will not allow the extradition out of Ireland, however, of anyone who successfully claims the crime he is accused of was politically motivated.

A suspect can legally be arrested and tried on either side of the border for a terrorist crime committed on the other side, but it is difficult to get witnesses and evidence across the border. There also is no channel of communication between British troops in Ulster and the Irish military. They must instead go through the cumbersome process of communicating across the border through their respective police forces.

The Protestant Ulster Defense Association, linked during the mid-1970s with retaliatory killings of IRA members and Catholics, again threatened yesterday to "take the law into its own hands" because of "the recent increase in violence perpetrated by the IRA murderers against our community.

"We have been reluctant to take such action," said a spokesman for the UDA, believed by officials to possess considerable resources for paramilitary violence, "but recent events have underlined the complete inadequacy of the security forces to deal with the situation and protect our people."

The 18 soldiers killed Monday with two more critically wounded, exceeded the British army's annual death toll in Ulster for every year since 1974. Before this year, the IRA was believed to have been badly depleted by arrests, deaths and infiltration by the security forces.

But it has come back reorganized into a leaner, cellular structure that is much more difficult to penetrate and more efficient to run. Each small cell of a handful of terrorists hidden under assumed names in Ulster and Ireland knows little about the rest of the several hundred active terrorists except for the orders it receives to strike.

Money from bank robberies and drug smuggling and weapons and technology from foreign sources were apparently stockpiled during the long period of relative inactivity before the IRA signaled its current offensive with two well-coordinated bombings raids on Ulster cities and towns last winter.

The soldiers killed Monday, including Lt. Col. David Blair, commanding officer of the First Battalion of the Queen's Own Highlanders, were ambushed by two massive bombs detonated 25 minutes and 100 yards apart in a hay truck and an abandoned stone house in County Down in Ulster very near the Irish border. When soldiers returned the fire of snipers who shot at them after the bombs exploded, they killed a 29-year-old British tourist, who happened to be the son of one of the queen's coachmen and had rushed to see what had happened from just across the border in Ireland.

Five hours earlier on the opposite coast of Ireland, another bomb blew up Lord Mountbatten's 29-foot fishing boat as it left the small harbor of Mullaghmore in County Sligo, Ireland, about 15 miles from the Ulster border. Mountbatten, 79, his 14-year-old grandson, Nicholas Knatchbull, and a 16-year-old helper on the boat, Paul Maxwell, all died in the explosion.

Today the 82-year-old dowager Lady Brabourne, mother-in-law of Mountbatten's daughter, Lady Patricia Brabourne, also died of her injuries, Lady Patricia Brabourne, 55, is still in critical condition in the intensive care unit of a Sligo hospital. Her husband, Lord Brabourne, formerly John Ulick Knatchbull, and their son, Timothy, the twin brother of Nicholas, were listed in satisfactory condition today.

Mountbatten was a second cousin and close adviser of the queen, the favorite uncle of her husband, Prince Philip, and a confidante of their son and the queen's heir to the throne, Prince Charles.

Heads of state all over the world continued to send their tributes and condolences to the queen today. Mountbatten, the allied supreme commander in Southeast Asia during World War II and later the last Viceroy of India, was credited with beating the Japanese in Burma and then with forging the independence of India and Pakistan from Britain.