(Adds comments from state media paragraphs 10-11,15, details)

By Telly Nathalia

JAKARTA, Jan 6 (Reuters) - Former Indonesian president Suharto, rushed to hospital in critical condition on Friday, is showing some signs of improvement but requires constant monitoring, hospital and medical officials said on Sunday.

Suharto, 86, was admitted to Jakarta's Pertamina hospital suffering from anaemia and low blood pressure due to heart, lung and kidney problems. He deteriorated rapidly on Saturday, and was given haemodialysis to remove excess liquid from his body.

"Suharto's condition is now showing some progress. In general, (he is) still weak," Djoko Sanjoto, acting director of Pertamina Hospital, told a news conference.

"The heart and lungs have shown some improvements, excess liquid in the whole body has started to decrease, especially in the lungs."

Suharto, a former general who ruled Indonesia with an iron fist for three decades until he was ousted in 1998, was accompanied by family members at the hospital.

A steady stream of important visitors including President Susilo Bambang Yudhoyono, former ministers and Muslim clerics visited him over the weekend -- a sign of his lingering influence among Indonesia's elite.

Yudhoyono said the government would give Suharto the finest medical attention available. As for all former leaders, "we always give the best medical treatment," the state-run Antara news agency quoted the president as saying.

"We have to pray that the actions taken by the medical team will work and we pray for the best for former president Suharto for the sake of all."

It was unclear how long Suharto would stay in hospital.

"We are not yet able to predict how long he will be hospitalised because we are still doing observations hour by hour," Djoko Rahardjo, co-ordinator of the presidential medical team, told the news conference.

"Because of his age, we are cautious about administering heavy medication that cannot be tolerated by his body."

The former president has suffered from various ailments in recent years, including intestinal bleeding and strokes, and has been admitted to hospital several times.

Suharto came to power after a botched 1965 coup attempt blamed on communists. In the aftermath of an event still shrouded in mystery, around 500,000 leftists were slaughtered across the country, crimes that remain unpunished.

He rarely appears in public and has lived in seclusion in Jakarta's leafy Menteng neighbourhood ever since he stepped down in the face of a tumultuous pro-democracy movement and an economic crisis.

He and his family are still involved in a couple of high-profile court cases, but the sudden deterioration in his health prompted some senior officials to call for legal proceedings against him to be dropped, Antara reported on Sunday.

Last year, the Supreme Court ordered Time magazine to pay Suharto more than $100 million in damages in a libel suit.

Time, which is challenging the ruling, published a May 1999 cover story that said Suharto and his family had amassed a fortune of around $15 billion. They have denied that.

Suharto was put on trial in the years after he was pushed from power on charges of embezzling hundreds of millions of dollars in state money, but the government dropped the case because of his poor health.

State prosecutors are now seeking a total of $440 million of state funds and about $1 billion in damages for alleged misuse of money held by one of Suharto's charitable foundations. (Writing by Sara Webb; Editing by Tim Pearce)

AlertNet news is provided by