* Italy coalition divided over ESM reform
* Opposition says Conte betraying country by not blocking it
* Reform bolsters bailout fund, facilitates debt restructuring
* Conte wants approval linked to other euro zone reforms (Re-leads with Conte's speech, combines stories, adds background)
ROME, Dec 2 (Reuters) - Prime Minister Giuseppe Conte told parliament on Monday a contested reform of the euro zone's bailout fund was in Italy's national interest, but that it should only be adopted as a package alongside other measures.
A reform of the European Stability Mechanism (ESM) is due to be approved by the bloc's countries this month, but Italy's right-wing opposition is against it and accuses Conte of "betrayal" by consenting to the changes without involving parliament.
"We can affirm that the negotiation conducted thus far has reached a balance in line with the national interest," Conte told the Chamber of Deputies, listing numerous occasions when he said he had informed parliament of progress in negotiations.
However, he said other measures, including a common bank deposit guarantee and a common unemployment insurance mechanism, need to be adopted along with the ESM changes, in addition to further progress on a euro zone budget.
Negotiations on these reforms are far less advanced and it remains unclear whether Conte is threatening to veto the ESM reform until they are passed, or merely wants informal guarantees on them from Italy's partners.
The ESM reform divides Italy's ruling parties. The anti-establishment 5-Star Movement is against signing off on it until plans for a wider European banking union become clearer, while the center-left Democratic Party (PD) supports the plan.
Conte, a technocrat who is not from either party, is trying to broker a deal between them while fending off fierce attacks from Matteo Salvini's right-wing League.
The coalition infighting could hinder plans by the euro zone's 19 member states to pass the reform, which it has been negotiating since early 2018.
The proposed reform of the ESM would give the fund more powers to handle financial crises, broaden the euro zone's monitoring powers over countries with economic imbalances and, if required, facilitate the restructuring of government debt.
Critics say the changes could make it more likely Italy will have to restructure, or even default on its debt, which is proportionally the highest in the euro zone after Greece's.
Conte said after meeting coalition officials late on Sunday that the dispute would be settled by a vote in parliament on Dec. 11.
Government officials told Reuters that Rome's main concern, on which it is ready to impose a veto, is to obtain a guarantee that sovereign bonds will not lose their status as risk-free assets under European banking union.
"In particular, what we don't want is that public debts are risk-weighted according to the credit rating of the countries, which would be very damaging for us," Maria Cecilia Guerra said on the margins of a conference in Milan.
This proposal was made last month by German Finance Minister Olaf Scholz in return for Germany potentially dropping its resistance to common deposit insurance.
In his speech in parliament Conte, often interrupted by opposition heckling, said Italy's public debt was "fully sustainable" and there was "no reason on the horizon" why it should need to seek assistance from the ESM.
He also said Italy would seek changes to a technical aspect of the reform which would require countries to issue bonds with conditions attached, known as "single-limb Collective Action Clauses," which would make debt restructuring easier.
These would prevent holdout investors blocking a debt restructuring to get a better deal.
Italy will push to make these CACs more flexible to protect small investors, Conte said, introducing a further element hindering smooth approval of the reform by the euro zone. (additional reporting by Angelo Amante and Andrea Mandala, editing by Alexander Smith, Christina Fincher, William Maclean)