The Scottish Green party has promised leftwing voters it would put Nicola Sturgeon under friendly pressure to tax the rich if it wins a large number of Holyrood seats in May.

Patrick Harvie, the party’s co-convenor, said raising tax rates to prevent spending cuts would be “agenda item one” if Sturgeon invited the Scottish Green party (SGP) into talks after the Scottish parliamentary election.

“Frankly I’m slightly astonished that the Scottish National party do seem to have walked away from the space to debate progressive tax policy,” Harvie said at the launch on Tuesday of the SGP’s Holyrood manifesto.

Sturgeon has rejected a new 50p top tax rate. In contrast, the SGP has proposed a 60p upper tax band for earnings over £150,000, with a new 43p rate for earnings over £43,000, allowing for tax cuts for all those below £26,500.

The Scottish Greens hope to win at least seven Holyrood seats, compared with two in 2007 and 2011, by positioning itself as a constructive if critical ally for the SNP in Holyrood. Its campaign logo is the white-on-blue cross of the Scottish saltire with the top triangle of the flag in green.

Alison Johnstone, who is defending her Holyrood list seat for the Lothians, said: “The green message has never been more relevant: our manifesto challenges austerity and it puts wellbeing at the heart of government. Our manifesto will not be delivered by a timid government, but it can be delivered by a government with vision, using the new powers fully that are coming our way.

“Greens will challenge the government to deliver a fairer, greener and healthier Scotalnd and we will support them when they strive to deliver these aims. Scotland’s parliament can be bolder: no one party can have all the answers.”

The party hopes radical pro-independence voters will give it their second, list vote, to act as the SNP’s conscience on issues such as higher taxes, a permanent ban on fracking (also proposed by Labour and the Lib Dems), land reform, increased public spending and a transition away from heavy reliance on North Sea oil jobs.

The SGP deliberately shied away from offering clear targets or strategies for shutting down North Sea oil production in its 48-page manifesto, despite arguing that two-thirds of the world’s fossil fuels were unburnable and having previously attacked SNP climate policies.

Instead, the manifesto effectively accepts that fossil fuels will remain a significant part of Scotland’s energy mix well into the 2030s. One SGP official said before the launch: “We can’t turn it [North Sea oil] off.”

It said 50% of all energy use in Scotland should be from renewables by 2030, and it has plans to create 200,000 jobs in renewables and oil decommissioning by 2035, in part by quadrupling green power supply from community-owned schemes to 2GW by 2030.

Harvie claimed the Scottish Greens could not campaign for a cut-off date for North Sea oil production because oil policy was set by Westminster. “A Scottish parliament is not in a position to set a timescale. What we do need to set is a direction of travel away from over-exposure to the carbon bubble and towards investment in the alternatives.”

SGP officials later said the party believed oil production should be slowly phased out, helped by part-nationalisation of oil wells and refineries, until there were about 10,000 North Sea jobs by 2035 – a timeframe that many oil economists already predict will see the industry naturally close to ending.

Opinion polls show the SNP is on course for its second successive majority government, winning up to 70 of Holyrood’s 129 seats on 5 May, but the SGP hopes to replace the ailing Lib Dems as the fourth party. Boosted by a tenfold leap in membership since 2011, following a surge in support from the independence referendum, the party is spending £350,000 on this year’s campaign – its largest budget yet.

The SGP manifesto puts heavy emphasis on increasing social care and welfare funding, including a 50% increase in carers’ allowances; a £9 an hour minimum for care workers; 4,000 extra teachers; a jobs, college or training guarantee for every school leaver; and a guaranteed bursary for every further education student and summer funding for students.

The manifesto did not put any costings on these policies other than confirming its tax plans would increase Holyrood funding by £2bn, and Harvie was unable to offer any costings at the launch.

SGP officials later said increasing the care allowance by 50% would cost £91m, and setting care workers’ wages at £9 an hour would cost £20m more. Giving all college students a bursary would require up to £4m a year, with about £120m needed to hire 4,000 extra teachers.