The local government minister said the situation is "very serious and needs to be addressed as a matter of urgency".Julie James was responding to an appeal by the council to send in an "honest broker" between Merthyr's leadership, opposition and top officials.
Council leader Kevin O'Neill called the current position "fractious"
Mr O'Neill said independent-controlled Merthyr needed "support with member interaction given the current fractious position and financial challenge".
In a statement to AMs, Ms James said an external advisor would look at "key challenges" facing Merthyr and what help it needs.
"an experienced political leader will work with Merthyr Tydfil council members to develop and strengthen working relationships across all political groups and between members and officers", she said.
In a letter to Ms James on 3 June, Mr O'Neill said the council faced "enormous pressure" to deliver social services to vulnerable people and asked for expert help on how to manage finances.He also said it was difficult to make changes "because of our political balance".
The council is led by independents, but with 16 of the 33 councillors they do not have overall control.
Labour is the biggest opposition group.
Mr O'Neill also refers to concerns raised by the Wales Audit Office (WAO), the public spending watchdog.
Council managers have met the WAO to seek advice after it warned the authority not to keep raiding its reserves.
Merthyr used £560,000 of its reserves last year to help plug a deficit - most of which was due to pressure on social services, in particular the budget for children in care.
The council expects to have a deficit of £8m in 2020, growing to £15m by 2022.
Arwyn Jones, BBC Wales political correspondent
What powers "an experienced political leader" (an his or he political affiliation if any) does not seem to be clear at the moment, but it does not the same as when In March 2011, after "years of political infighting" Isle of Anglesey County Councilt became the first council in British history to have all executive functions suspended, with a team of commissioners appointed by the Welsh government put in place to run the council's functions with elections ultimately delayed, meaning they took place a year after the rest of Wales, pending a new electoral system.
It seems that what has happened in Merthyr is that the pressures of cuts to its budgets have run into a failure of councillors to work together.There are 33 councillors at the authority, but the independent group who run the administration only has 16 of them. This means they have had to rely on support from opposition members to pass budgets and make decisions on how to spend money.
Two months ago, Wales' spending watchdog raised serious concerns that the council was dipping too far into its reserves to pay for the higher costs of social services for children, saying it was not "viable" to continue as it had done.
But now the ruling group and the opposition cannot agree on what to do next, so the Welsh Government will appoint, basically, a peace envoy to see how a deal can be reached.
I cannot think of a time when another council has asked for help in this way, even though minority administrations are hardly rare in local government; that's how 10 of the 22 in Wales were run after the last elections, two years ago.
Previous attempts to merge Merthyr with the much larger Rhondda Cynon Taf and whilst some mat think this may be the solution, I suspect RCT would baulk at inheriting Merthyr's deficit.
So whats the solution Is upose Labour would probably claim if the were to form a Majority administration they would resolve the issue but , then it would mean imposing cuts that some of its members would resist.
Quite frankly this blogger is at a loss , to see any solution and am worried that it could end up with the "an experienced political leader or honest broker" could end up the real power in the County Borough"
Something that could set a dangerous undemocratic precedent.