* NATO chief accuses Russia of "reckless" policy in Ukraine
* Support for rebels growing in "scale and sophistication"
* Ukrainians lose more soldiers in overnight fighting (Adds rebels bringing down Ukrainian warplane, paras 5 and 6)
By Richard Balmforth and Pavel Polityuk
KIEV, Aug 7 (Reuters) - The head of NATO called on Russia to "step back from the brink" of war by pulling its troops back from the Ukrainian border and warned further intervention in Ukraine would bring it greater isolation in the world.
Anders Fogh Rasmussen, the U.S.-led alliance's secretary general, made his call on Thursday during a visit to Ukraine in a show of solidarity after NATO warned of a possible invasion by Russia which, it said, had massed 20,000 troops near the frontier.
Saying Russia's support for the rebels was growing in "scale and sophistication", Rasmussen said: "I call on Russia to step back from the brink, step back from the border and not use peacekeeping as an excuse for war-making."
Earlier, he and Ukrainian Prime Minister Arseny Yatseniuk discussed possible Western alliance support for Ukraine's defensive strength - excluding lethal aid - even as the Kiev government's forces continued losing men in clashes with pro-Russia separatists in the Russian-speaking east.
Rebels brought down a Ukrainian Mig-29 fighter plane with a missile on Thursday evening, Ukraine's military information spokesman Vladyslav Seleznyov told Interfax news agency.
The plane came down near Horlivka, about 100 km (60 miles) from the border with Russia. The plane's crew managed to eject from the aircraft, he said.
The Kiev government announced it was suspending a ceasefire with the rebels at the crash site of the Malaysian airliner that was shot down on July 17, after an international mission halted recovery work there for security reasons.
Defence spokesman Andriy Lysenko told journalists that government forces had clashed 19 times with separatists in the 24 hours up to Thursday morning, often coming under artillery and missile fire from within Russian territory.
"In the past 24 hours we have lost seven servicemen, and 19 received wounds," Lysenko said.
Regional authorities in Donetsk, the east's main industrial hub and now the main rebel redoubt, said one person had been killed at a medical facility when a shell struck on Thursday after a night of intensive artillery attacks.
Government forces, who say they are gradually tightening a noose around the rebels, denied responsibility. "We have accurate information that the Ukrainian military are not shelling those areas," said Lysenko.
Rasmussen said the downing of flight MH17 with the deaths of all 298 people on board was a tragic consequence of Russia's "reckless" policy in Ukraine and he urged Moscow to end its support for the separatists and engage in "sincere dialogue" to bring peace.
Rasmussen, at his meeting with Yatseniuk, discussed the possibility of a proposed NATO trust fund to support Kiev's capabilities in such areas as command and control, communications and cyberdefence, the government said.
But the provision of lethal aid to Ukraine by the military alliance did not appear to have been discussed.
Asked about this at the news conference, said it was not a question for the alliance as such but for its individual members.
The new deaths among government forces suggest Kiev's military losses now total more than 400 since the conflict with the pro-Russian separatists erupted in April.
The United Nations High Commissioner for Human Rights says the conflict has cost the lives of more than 1,100 people in all, including government forces, rebels and civilians.
Ukraine and its Western allies accuse Russia of orchestrating the revolt and arming the rebels, who have declared independent "people's republics" in the two main industrial regions. Moscow denies involvement.
The United States and European Union have imposed sanctions on Russia which Rasmussen said would broaden and deepen if it stepped up its intervention in Ukraine. Moscow has retaliated with a sweeping ban on imports of many Western foodstuffs.
Fighting has intensified since the shooting down of flight MH17, an act the West laid at the door of the rebels. Russia and the rebels blame the disaster on Kiev's military offensive.
STEADY GOVERNMENT GAINS
The Netherlands, which lost 196 citizens in the incident, said on Wednesday it was halting the recovery of debris and victims' belongings because of continued fighting in the area.
The Ukraine government said it would suspend a ceasefire now in the area until an international team of experts was ready to resume recovery work there.
Despite a steady loss of lives, government forces have been gaining gradually against the rebels, who have been mainly led until now by Russian citizens and are armed with tanks, artillery and other heavy weapons that Kiev says have been brought across the border from Russia.
Sources told Reuters the main rebel leader in the city of Donetsk, a Russian, may now be replaced by one of the separatist commanders who is a local man. Rebels said this was being discussed but could not be confirmed.
Russia announced military exercises near the border this week, and Western officials fear Russian President Vladimir Putin could order Russian forces into Ukraine if he sees that the rebels are about to be crushed. (Additional reporting by Natalia Zinets in Kiev and Anton Zverev in Moscow; editing by Andrew Roche)