David Lidington insisted he was not issuing threats to the upper house as he stressed peers needed to listen to the strength of feeling in the elected wing of Parliament.
He told the BBC's Andrew Marr Show: "I am not standing, sort of, round the back alley, you know, waiting for a stray peer to arrive having a cosh in my hand.
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"Of course they are free to propose and debate amendments, I hope they will also take full account of the strength of opinion form the elected House.
"We have got a constitutional process, and I think the fact the exit Bill has gone to the House of Lords - Article 50 Bill - with a majority of more than 300 from the Commons, and unamended, and frankly, the amendments were all defeated by majorities well in excess of the Government's normal majority, is a pretty powerful message to the Lords."
Some pro-Leave Tories have called for major reforms of the Lords if peers try to thwart the will of the Commons on the Brexit Bill which gives Prime Minister Theresa May the power to trigger Article 50 of the Lisbon Treaty and formally begin the two-year withdrawal negotiation process with the EU.
Mr Lidington added that MPs would get the chance to "probe" the Government stance during the negotiations, and vote on various aspects of policy as legislation is introduced to take back powers from the EU
"There will be plenty of opportunities for votes. Obviously, the precise nature of the issues to be determined by those votes depends on what the motions are, and what the amendments are."
Liberal Democrat leader in the Lords, Lord Newby, said the notion peers would block the Bill by voting through amendments was an "Aunt Sally".
His party want to include a second public vote on the final Brexit deal and also a guarantee for EU nationals living in the UK.
Lord Newby told Sky's Sophy Ridge: "If you take the amendments we are going to be pressing they don't have that effect at all.
"Passing these amendments does not delay the process for a second."
But former Conservative chancellor Lord Lamont said he feared some were tabling amendments in order to "scupper" the Government's negotiations.
He told the broadcaster: "I think a lot of the amendments that are put forward are really designed to obstruct the Bill and everybody knows that if the Bill is delayed that will scupper the whole negotiation.
"I'm not saying that's Lord Newby's motive but I think it's the motive of some of the people coming forward with these amendments - it's to get embroiled in a time wasting, time delaying exercise."
He said any perceived blocking by the upper house would cause "outrage" and could prompt calls for reform.