Scottish Labour’s executive has rejected its leader’s proposals for a special conference on federalism, which could have seen it support a multi-option referendum on independence.

The Guardian revealed on Thursday that Scottish party leader Richard Leonard wanted to produce a detailed proposal for a federal UK as Labour’s alternative to full Scottish independence, and put that to a party conference in May.

A Scottish Labour source said: “Labour would be more willing to consider supporting a second referendum if it was multi-option,” provoking a furious backlash within the party.

During a tense meeting on Saturday, the Scottish executive committee (SEC) rejected Leonard’s proposals and instead voted to hold its own “away day”, in private, to define federalism and draft policy on it.

That has delayed a decision on whether to ask for federalism to be included as a third option in a multi-choice independence referendum, alongside full independence or keeping the UK’s current structure.

A party source insisted Leonard’s idea of having a special conference was not a formal proposal, and was always subject to SEC approval. However, other sources say Leonard tabled the idea at both a shadow cabinet meeting at Holyrood on Monday, and then argued for it as Labour’s Holyrood group meeting on Tuesday.

The SEC met at Labour’s Scottish headquarters in central Glasgow as tens of thousands of people joined a pro-independence march through the city, although a planned rally in Glasgow Green was cancelled due to high winds and heavy rain.

Thousands of campaigners for Scottish independence wave flags as they march through Glasgow. Photograph: Robert Perry/EPA

Leonard has come under immense pressure to respond to Scottish Labour’s dire election results in the December general election, after the party was again left with one Scottish MP after its worst election result in recent history, polling 18.6%.

Nicola Sturgeon, the first minister and Scottish National party leader, said her party’s victory in 48 of Scotland’s 59 Westminster seats, with 45% of the vote, proved the electorate supported her calls for a second independence vote this year.

That demand has been repeatedly rejected by Boris Johnson, the prime minister, with opinion polls not yet showing majority support for leaving the UK.

A series of Labour figures, including several defeated Scottish MPs and Clive Lewis, an outsider in the race to replace Jeremy Corbyn as UK party leader, have said the party needed to accept the case for a referendum, and also consider splitting away from the UK party.

Ben Bradshaw, the former Labour cabinet minister, told the German newspaper Der Tagesspiegel he was “100% certain” Scotland would vote for independence. He added: “The political class in England – and this includes my own party – must very quickly recognise the Scots’ right to self-determination”.

Scottish Labour had gone into the election with a manifesto pledge to abolish the House of Lords and replace it with a federal “senate of the nations and regions”. If Labour had won the election, it said a federal system would be introduced after a UK-wide constitutional convention.

The UK party’s manifesto did not refer to federalism, but endorsed the constitutional convention proposal and replacing the Lords with a senate of nations and regions.

Scottish Labour had backed federalism in 2017, as had Leonard’s predecessor Kezia Dugdale, but December’s election was called before Leonard was able to publish a detailed policy on how federalism would work which was being written by Lady Pauline Bryan.