Ahead of a Cabinet meeting, Mr Johnson is expected to argue the unions are "harming the very people they claim to be helping" and to call for a "sensible compromise". Thousands of union members are expected to walk out this week, with just one in five trains running on strike days.
Boris Johnson will condemn unions for what is expected to be the biggest train strike in three decades.
Around 50,000 members of the Rail, Maritime and Transport (RMT) union at Network Rail and 13 train operators will walk out for all of Tuesday, as well as Thursday and Saturday in a dispute over pay, jobs and conditions.
Just one in five trains will run on strike days, mainly on main lines, and then only for around 11 hours.
Network Rail has warned the industrial action will cause six days of disruption because of the knock-on effect on services on the days in between.
Ahead of a Cabinet meeting on Tuesday, the prime minister will argue the unions are "harming the very people they claim to be helping" and will call for a "sensible compromise".
There will also be a strike on the London Underground on Tuesday by RMT and Unite union members, in a separate row which will cause major disruption to the Tube.
Talks to avert the rail strike were held until Monday afternoon, but remained unresolved - with both sides blaming each other for the lack of a breakthrough.
The RMT union is asking for a pay rise of 7%, which is lower than inflation but higher than that offered by employers.
RMT general secretary Mick Lynch said the dispute could drag on for months, adding: "It is clear that the Tory government, after slashing £4bn of funding from National Rail and Transport for London, has now actively prevented a settlement to this dispute.
"The rail companies have now proposed pay rates that are massively under the relevant rates of inflation, coming on top of the pay freezes of the past few years.
"At the behest of the government, companies are also seeking to implement thousands of job cuts and have failed to give any guarantee against compulsory redundancies."
The prime minister is expected to accuse unions of "driving away commuters who ultimately support the jobs of rail workers" while hitting businesses across the country.
He will say: "Too high demands on pay will also make it incredibly difficult to bring to an end the current challenges facing families around the world with rising costs of living.
"Now is the time to come to a sensible compromise for the good of the British people and the rail workforce."
Downing Street said ministers at Tuesday's meeting would discuss the rail strikes and also the tough economic climate facing the country.
Chancellor Rishi Sunak and the prime minister are expected to argue pay discipline and restraint are important to manage inflationary pressures downwards.
"We have a responsibility to tackle inflation and stop it becoming entrenched," No 10 said.
"To do this we must ensure that pay settlements are sensible and do not scramble to match inflation, and as a result drive up prices as the cost of goods and service increase to incorporate pay rises."
Speaking ahead of the meeting, Mr Johnson said: "It is right that we reward our hard-working public sector workers with a pay rise, but this needs to be proportionate and balanced.
"Sustained higher levels of inflation would have a far bigger impact on people's pay packets in the long run, destroying savings and extending the difficulties we're facing for longer."