The statement, sent to the left-wing Greek newspaper, Eleftherotypia, came as officers from Scotland Yard's anti-terrorist branch and UK Foreign Office investigators travelled to Greece to help with the inquiry.
The group accused Brigadier Stephen Saunders of helping to co-ordinate Nato's bombing of Yugoslavia.
But a British official described this as absolute nonsense. A Ministry of Defence spokesman described the allegation as "utter fantasy" and "absolutely without foundation". He said the brigadier was with the UN observer mission on Iraq when the bombing of Kosovo started.
Greek sympathies
Brigadier Saunders was shot dead by two people on a motorbike on Thursday morning on his way to work at the British Embassy.
Security for the visiting British defence procurement minister, Baroness Symons, and embassy staff has since been stepped up.
The Greeks sympathised with the Serbs because of their shared Orthodox Christian heritage and their common hostility to Turkey, which has historical links with the ethnic Albanian Kosovars.
Guerrillas' statements
In its 17-page statement, November 17 also said it carried out a series of attacks attributed to it by police in the spring of 1999 in which no-one was killed.
These included rocket attacks on branches of three foreign banks and against the residence of the German ambassador to Athens.
November 17 is a Marxist Leninist group, but in recent years its statements have taken on an increasingly nationalistic tone.
The UK Foreign Office denied that British security officials had been sent to press Greek investigators to find the diplomat's killers.
No member of November 17 has been caught despite the group's 25-year campaign.
"Greece invited us to send out policemen to provide expertise and help with any information that might be useful to them," a spokesman said.
"A Foreign Office security expert is going out to review the security of the embassy and embassy staff," he added.
Olympic worries
The killing prompted wide calls for Greece - which has a lacklustre record in tracking down terrorists - to hunt down the killers.
Police said ballistic tests showed the spent shells from a .45 calibre automatic pistol found on the scene came from a weapon used by November 17 in previous attacks.
The group has killed three Greeks and an American with the same gun since 1980 and wounded a Greek parliamentary deputy.
Brigadier Saunders, 52, who leaves a widow and two teenage daughters, is its 23rd victim.
With international concerns high about security for the 2004 Olympic Games, the Greek Foreign Minister George Papandreou promised "to do everything possible to bring the perpetrators to justice".
A US congressional commission report last week proposed sanctions against Greece and Pakistan for "not co-operating fully" in efforts to stamp out terrorism.
The US State Department described Greece as "one of the weakest links" in anti-terrorism efforts in Europe.