Players who joined the Saudi-backed LIV Golf series "knew there would be consequences if they chose money over competition", says DP World Tour chief executive Keith Pelley.
Pelley has issued a statement responding to that threat.
"It is not credible that some are now surprised with the actions we have taken," he said.
A number of players have been enticed to leave the established DP World and PGA Tours for the new eight-event series, which boasts a £200m prize fund. They include Britons Lee Westwood and Ian Poulter, and Americans Brooks Koepka, Phil Mickelson and Dustin Johnson who have won 12 majors between them.
The inaugural event of the Saudi Arabian-backed LIV Golf series took place in June at Centurion Club in Hertfordshire.
The second one is taking place in Portland, Oregon, from 30 June to 2 July.
The DP World Tour - formerly the European Tour - banned players who competed in the first event from next week's Scottish Open and fined them £100,000.
At the time, it also warned players that "participation in a further conflicting tournament or tournaments without the required release may incur further sanctions".
The PGA Tour similarly suspended 17 of its members who played in the inaugural LIV Golf event.
"There has been a leak to the media of a letter we received on behalf of a number of LIV Golf players which contains so many inaccuracies that it cannot remain unchallenged," said Pelley of the letter from 16 LIV golfers.
"Before joining LIV Golf, players knew there would be consequences if they chose money over competition. Many of them at the time understood and accepted that."
The DP World Tour and PGA Tours have strengthened their alliance to try to fight off an "existential threat" posed by LIV Golf in a move that brings the two circuits closer together until at least 2035.
"We also take great exception to an allegation made near the end of the letter which states we are somehow playing 'second fiddle' to the PGA Tour," said Pelley.
"Nothing could be further from the truth.
"The letter also expresses supposed concern about the future of the DP World Tour. Rest assured no-one should have any worries on that score."
He added: "The sanctions for those members who knowingly broke our rules by playing at the Centurion Club without a release are proportionate, fair and, I believe, considered necessary by the majority of our members."
As well as objections of the LIV series coming from inside golf, it has drawn criticism for its Saudi funding because of the Gulf state's human rights record.
The opening round of the latest event in Portland was marked by protests on Thursday by family members of people killed in the 11 September, 2001 attacks in the United States.
The 9/11 terror attacks on the United States in 2001 killed almost 3,000 people and according to an FBI declassified document, 15 of the 19 plane hijackers in the attack were Saudi nationals.