WASHINGTON, Dec 18 (Reuters) - When the Pentagon pulled the world's biggest defense contractors into a meeting to tell them to ramp up production shortly after Russia invaded Ukraine, one CEO hesitated, saying they did not want to be stuck with a warehouse full of rockets when the fighting stopped, according to three people familiar with the discussion.

Nearly two years later, big defense firms are singing a different tune, with several expecting strong demand in 2024 as the U.S. and its allies load up on expensive weaponry and munitions with an eye on what they perceive as more aggressive actions from Russia and China.

The math is simple. For example, to meet demand for missile defenses, production of Patriot interceptors for the U.S. Army - a projectile fired at an incoming missile with the aim of knocking it down - will rise from 550 to 650 rockets per year. At around $4 million each, that's a potential $400 million annual sales boost on one weapons system alone.

Since increasing production volumes of older systems is always more profitable than the high investment costs associated with ramping up production of new systems, stronger demand will flow quickly to the corporate bottom line.

Shares of the biggest defense companies, which have handily beat the benchmark S&P 500 stock index for the last two years, are expected to keep rising, according to Wall Street estimates.

Lockheed Martin, General Dynamics and Northrop Grumman shares are forecast to rise between 5% and 7% over the next 12 months, while the S&P is seen making limited gains.

US weapons stockpiles were not "full" before Russia invaded Ukraine, said Eric Fanning, chief executive of the U.S. Aerospace Industries Association, and "adversaries are seeing our stockpiles starting thin and being depleted." As a result, demand is being driven by Chinese aggression, fear about Russian aggression and to support allies in the Middle East, he said.

PATRIOTS AND ROCKET MOTORS

Patriot systems production can be broken down to show how sales of basic items will impact a range of companies. To start, RTX manufactures the radars and ground systems, and Lockheed Martin manufactures the latest generation interceptor missiles.

RTX boosted launcher and control system production to 12 units a year. A launcher and radar together cost around $400 million each.

Boeing has said over the next few years it will increase its Huntsville, Alabama, factory production capacity for sensors that are used to guide Patriot missiles by more than 30%.

Another strong demand signal can be seen in the backlog of solid rocket motors which are used by the vast array of arms in high demand since Russia's full scale invasion of Ukraine in February 2022.

The U.S. has two main rocket motor makers, Northrop Grumman, and L3Harris Technologies, which both said they have seen demand increase.

Northrop said much of the increase is due to demand for its rocket motors and warheads in the Guided Multiple Launch Rocket Systems (GMLRS) which are heavily used in Ukraine.

GMLRS are GPS-guided rockets with 200-pound (90kg) warheads. Lockheed Martin makes 10,000 of the missiles per year and is increasing production to 14,000. They have an average cost of $148,000 each according to Army documents and more than 6,100 have been sent to Ukraine so far, according to a Reuters analysis.

"Each day the munitions are being fired reinforces the need for substantive stockpiles," Tim Cahill, who runs Lockheed's Missiles and Fire Control business - a prime contractor for Patriot interceptors and GMLRS - said in a Reuters interview. "And I don't see that going down."

An executive at a rocket motor maker said the administration of President Joe Biden prioritized munitions in its 2024 Pentagon budget request.

He expected a boost to order backlogs once contracts came through following the passage of the $886 billion defense policy bill known as the NDAA, or National Defense Authorization Act. It was approved by Congress last week and Biden is expected to sign it into law. (Reporting by Mike Stone in Washington; editing by Chris Sanders and Grant McCool)