The embattled premier suffered a major parliamentary rebellion on the cash-for-reforms deal last week, with a fifth of the lawmakers from his radical-left Syriza party voting against sweeping changes to Greece's taxes, pensions and labour rules. He was forced to rely on the support of opposition MPs to get the law passed.
The second bill is less controversial, with MPs set to vote on measures including an EU directive that guarantees bank deposits up to 100,000 euros (USD 108,000), as well as civil justice reforms designed to speed up legal proceedings and reduce their costs.
The prime minister received a boost Tuesday when Standard & Poor's raised its credit rating on Greece by two notches to CCC+ from CCC-, still in junk territory but a step in the right direction.
S&P said that the scenario of Athens defaulting on its debts was no longer inevitable in the coming year and thus the chances of Greece having to pull out of the euro were reduced, though still "high".
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Tsipras said he had read all the "heroic declarations" from his critics about the path he should have taken, but insisted there was "no alternative solution".
"I am aware of the responsibility I have taken in making a difficult compromise," he told colleagues at a meeting yesterday.
He reshuffled his cabinet just before the weekend to fill the vacancies left by the MPs who were sacked after voting against the first wave of reforms. He made nine changes overall.