The Lord President, Lord Gill, snubbed Holyrood on the grounds of "constitutional principle", despite agreeing to appear at another parliamentary committee debate this week on court structures.
MSPs have described the rejection as "disappointing", an "insult" and smelling of "vested interests".
Legal campaigner Peter Cherbi last year lodged a petition at Holyrood calling for the members of the judiciary to declare their financial interests and any hospitality received. He argued that this could "provide greater transparency within the judicial system" and avoid conflicts of interest.
Such a register could require judges to declare shareholdings and property ownership.
A range of public servants, including MPs, MSPs and quango board members, already have to file to a register of interests.
In the course of considering the proposal, Gill, who became Lord President last year, wrote to the Petitions Committee that a register was "unnecessary".
He said there were "sufficient safeguards" to ensure judicial impartiality and argued that judges' privacy could be affected by "aggressive media or hostile individuals".
He concluded: "The establishment of such a register therefore may have the unintended consequence of eroding public confidence in the judiciary."
In March, the committee asked the Lord President to give oral evidence but he declined, saying that he could "not add any material points" to his written response. Weeks later, the committee's convener, Labour MSP David Stewart, asked Gill a second time to appear, suggesting that his evidence would help the inquiry.
However, Gill again refused. He wrote that he intended "no discourtesy" and noted that judges had in the past given evidence to Holyrood committees. But he argued that participation must "be kept within prudent limits".
And he cited a section of the Scotland Act 1998 – the legislation that lays down the Parliament's powers – which states that judges may not be required to give evidence.
He wrote: "This is not a loophole. It is a necessary part of the constitutional settlement by which the Parliament is established. Its purpose is to protect the independence of the judiciary."
Gill said he was open to a meeting with the committee convener about the implications of his invitation, rather than to discuss the petition.
However, he has agreed to give oral evidence to the Justice Committee on Tuesday on proposals to shake up the court system. Last year, he also gave evidence to that committee about legislation on civil justice.
According to Section 23 of the Scotland Act, Holyrood may require "any person" to attend its proceedings for the purpose of giving evidence. However, this legal power cannot be "imposed" on a judge.
At a meeting of the Petitions Committee, Conservative MSP Jackson Carlaw said: "The student anarchist in me smells the whiff of vested interests closing doors and turning their backs in an effort to shut the matter down. In fact, the protest was so great that I found myself thinking, 'Methinks the Lord President doth protest too much'."
The Cherbi proposal is partly motivated by the Parliament of New Zealand debating a register of judges' financial interests. In 2010, a former Supreme Court judge in New Zealand resigned after he failed to disclose a debt owed to a solicitor who appeared in one of his cases.
SNP MSP Chic Brodie, deputy convener of the Petitions Committee, said: "It's regrettable that Lord Gill feels he cannot discuss the register of interest issue, but at least there is an opportunity for a meeting."
A spokesperson for the Judicial Office for Scotland declined to comment.