Mr Andrews said he discussed the fabricated picture – which depicted an Australian soldier with a knife to the throat of an Afghan child – with Mr Morrison on Tuesday.
"That [image] was just beyond the pale. It's wrong. I condemn it," Mr Andrews said on Wednesday morning.
But asked if he was reconsidering the Belt and Road agreement in the light of its publication on Twitter and China's aggressive escalation in rhetoric since, the Premier had a one-word answer: "No".
An hour earlier one of Mr Andrew' ministers, who was involved in negotiating the state's controversial deal, had been unwilling to personally denounce the Tweet posted by a spokesman for China's Foreign Affairs Ministry.
The Premier said both he and Mr Morrison hope that the countries' relationship could be healed soon and Mr Andrews repeated his wish that China tone down its "inflammatory language" and work on improving bilateral ties as soon as possible.
"This relationship is far too important to farmers, to manufacturers, to workers, to profits for Victorian companies and therefore prosperity for our state," Mr Andrews said.
"This is not just our biggest customer, but it is all about jobs. We need a good relationship but it has to be a fair and respectful one."
Mr Andrews said China had led the way in causing the relationship to deteriorate this week.
"That's no way to run a productive partnership and I'd simply say that the time has come, surely now, for everyone to take a breath, to sit down and to work through the issues," the Premier said.
"I'm confident that the Commonwealth government knows and understands how important this relationship is. I'm certain of that ... and I'm not going to be telling the Commonwealth government how to do their job".
Mr Andrews also took a swipe at new federal government laws, set to be passed this week, that will give it the power to scrap agreements struck with foreign governments by states, local councils and universities.
Victoria signed a memorandum of understanding with China on the Belt and Road initiative in 2018, which the Commonwealth will probably be able to tear up once the new laws, currently being negotiated with the federal Labor Party, pass.
With China imposing trade restrictions that threaten up to $20 billion of Australian exports, the state opposition has questioned the deal's benefits, but Mr Andrews said he wouldn't have entered into the agreement unless he believed it was in Victoria's best interests.
The Premier also criticised the scope of the impending laws that would allow them to review agreements such as sister city relationships.
"Like, matters of massive international intrigue like sister city arrangements. Who Dandenong is the sister city with. Who Monash, where I live, is the sister city with," Mr Andrews said.
"The federal parliament can do as they please. They are accountable for the decisions they make. If this is the biggest and most important thing for them to be doing at the moment, well, I look forward to them explaining that to everybody."
An hour earlier Danny Pearson, the Minister for Government Services and Creative Industries refused to criticise the Tweeted image.
"I think the Prime Minister has already made some comments around that," Mr Pearson said, referring to Mr Morrison calling it "truly offensive" and "repugnant".
Mr Pearson was the Premier's parliamentary secretary until he was promoted to the ministry in June and accompanied Mr Andrews to China on more than one occasion to broker the Belt and Road memorandum of understanding.
Asked whether Victoria should play a more prominent role in the Australia-China relationship because of the agreement, Mr Pearson said the federal government "has made it clear they want to have a dominant role on these questions from a foreign policy perspective".
"From a Victorian perspective, we are very focused on trade. We want more trade, more trade means more jobs," Mr Pearson said.
"We're very focused on working closely with our trade partners."
Victoria renewed the agreement in October last year and was due to sign a third deal this year, which has been delayed due to the coronavirus pandemic, although Mr Andrews has previously indicated he intended to go ahead with it when possible