Members of such schemes will be facing bigger tax bills if they fail to take up the chance to pay up, HMRC warned.
The total amount of tax owed by these users is £430 million.
Officials estimated that on average, each of the users of the contractor loan schemes covered by this settlement opportunity owes £11,000 a year in tax.
The schemes, described by HMRC as "particularly aggressive", are used by a small minority of contractors to "avoid paying their fair share".
They involve complex arrangements with individuals signing a contract of employment with an offshore employer.

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The contractor then receives their pay through the offshore company or trust as what is claimed to be a non-taxable loan, rather than income.
Users will have until January 2015 to take the offer of a settlement. If they do, they will pay the tax and interest due on the sums they received as loans under the scheme.
If they continue to challenge HMRC in the courts, they risk having to pay additional tax charges and penalties – as well as the costs of litigation if they lose.
Jennie Granger, HMRC director general for enforcement and compliance, said: "Many people regret ever getting involved with complex aggressive tax avoidance schemes and HMRC is providing an opportunity for contractors to come forward and straighten out their tax affairs.
"This is an important opportunity and we are working hard to encourage users to withdraw from such schemes. We also want to ensure they've understood our position.
"They can choose to continue to litigate for a better outcome but they risk a worse result.
"HMRC has a strong track record of winning tax avoidance cases in court, with around 80% of decisions in our favour. The costs for users are high, potentially resulting in penalties, charges and significant legal costs for scheme users."