The court refused permission to Salvatore Girone to travel to Italy for Christmas.
It also rejected Massimiliano Latorre's request to extend his stay in Italy by two more months. He was allowed to go home in September for four months for medical treatment.
The marines are on bail pending trial.
On Tuesday, the court said the trial had already been much delayed and that legal proceedings must resume soon.
The marines were guarding an Italian oil tanker when they opened fire, killing two men off the Kerala coast. The marines said they mistook the fishermen for pirates.
India has ruled out the possibility of a death penalty and invoking the anti-piracy law to try the marines.
Italy has always insisted that as the shooting had taken place in international waters, the men should be tried in Italy.
Last year, Delhi and Rome were involved in a bitter diplomatic row after Italy refused to send the marines back when they were allowed to go home to vote in the February 2013 elections.
The marines eventually returned to Delhi a month later and the court withdrew its controversial order.

The 23-year-old from Westmeath beat Gadzhimagomedov on a unanimous 5-0 points decision in the Ukraine decider.
Kurt Walker and Brendan Irvine had to settle for bronze medals after losing their semi-finals on Friday.
Lisburn bantamweight Walker was beaten by Mykola Butsenko while Belfast flyweight Irvine lost to Niall Farrell.
Walker and Irivine were both defeated on a unanimous decision.
Belfast light-welterweight Sean McComb missed out on a bronze medal after losing to England's Luke McCormack in the 64kg division on Wednesday.
McComb suffered a narrow 3-2 split decision loss in the 64kg division.
All four Irish boxers have ensured a place at August's World Championships in Hamburg by virtue of having reached the last 16.

The Cambridge history student knew the "significance" of the monument but did not realise he was dangling from a war memorial, the Court of Appeal was told.
Gilmour, of Billingshurst, West Sussex, was jailed for 16 months for violent disorder in July.
The 21-year-old is appealing against his sentence.
Judges heard Gilmour had taken LSD and valium before joining the central London protests against increased tuition fees last December.
He was seen hanging from a Union flag on the Cenotaph and leaping on to the bonnet of a Jaguar - part of a royal convoy.
Gilmour was previously found by a judge at Kingston-upon-Thames Crown Court to have thrown a rubbish bin at the vehicle.
His lawyers are also challenging this ruling as part of the appeal.
The crown court judge had accepted that the incident at the Cenotaph did not form part of the violent disorder, but described it as "outrageous and deeply offensive behaviour".
During his several-hour-long rampage, Gilmour was also found to have kicked the window of Topshop's flagship store on Oxford Street.
He ended the day in possession of the leg of a mannequin.
Gilmour's defence QC, David Spens, said his client did not know what the Cenotaph looked like and, as he had lived "without a television for 10 years", this was "not actually as surprising as might have been thought".
The court heard he had turned to drink and drugs after being rejected by his biological father, the writer Heathcote Williams.
Mr Spens said he had "successfully reformed and rehabilitated himself" and addressed the "underlying drug and alcohol problems".
He added: "My submission is that this sentence was unduly harsh, unnecessarily so."
The court has reserved judgement pending other Court of Appeal rulings relating to the August riots, which may have a bearing on Gilmour's case.
India's Supreme Court has rejected travel appeals of the two Italian marines accused of killing two Indian fishermen in 2012.
[NEXT_CONCEPT]
Ireland's Joe Ward has won a third European Championship light heavyweight gold medal after defeating Russia's Muslim Gadzhimagomedov in the final.
[NEXT_CONCEPT]
Charlie Gilmour, the son of Pink Floyd guitarist David Gilmour, was unaware he was swinging from the Cenotaph during student protests, a court has heard.