The 10-year borrowing rate for France surged to 3.50 percent and for Spain to about 6.30 percent.
The latest ratcheting of tension reflects highly nervous investor sentiment despite progress in Italy and Greece towards new drives to reform public finance and the economies under new governments.
Spain is locked in a general election campaign expected to lead to a landslide against the governing Socialists.
The critically important gap between the rates paid by Germany and France, the two pit props holding up the eurozone, widened to 172.6 basis points or 1.726 percentage points, above the previous record of 170.2 basis points reached last week.
The French borrowing rate rose sharply to 3.500 percent and the German rate fell to 1.775 percent, meaning that France has to pay about twice as much as Germany to borrow.
The French rate had closed at 3.424 percent on Monday. The German rate had ended at 1.781 percent.
This is a closely watched indicator of convergence -- or in this case divergence -- in confidence regarding the German and French economies, and in political ability to control public finances in weaker countries.
Each rise of one percentage point in the cost of issuing new debt, or refinancing maturing debt, if sustained, adds huge amounts to the annual cost to taxpayers of funding borrowing.
Both Germany and France have the top AAA credit rating, but France now has to pay about twice the rate Germany pays to borrow money for 10 years.
The French government has said it will do everything necessary to retain its AAA rating which is widely considered to be at risk.
The EFSF rescue fund mechanism at the centre of the EU architecture to shore up the eurozone depends in large measure on France holding back pressure on the bond market.
Another measure of the acute tensions bubbling in the eurozone was the widening of the gap between German and Spanish borrowing rates.
The gap widened to 452.2 basis points or 4.522 percentage points, exceeding a previous record set on Monday.
The cost of 10-year borrowing for Spain was about 6.3 percent, a level considered to be at the limit or beyond what Spain can afford to finance its public deficit and refinance debt. It had closed at 6.106 percent on Monday.
The equivalent gap between German and Spanish borrowing rates also widened to a record, further signalling great anxiety about the components of the eurozone debt crisis as Italy and Greece head towards new budget reforms under new governments.
At Moneycorp in London, analysts commented that investors "appear to have pulled stumps on their brief honeymoon with the new technocrat masters in Athens and Rome."
They said investors "could not fail to notice how yesterday's 'successful' auction of five-year Italian government bonds delivered a yield of 6.29 percent."
Investors and people managing savings are buying German bonds, the low-risk benchmark in the eurozone, as a protection against risk.
This has the effect of pushing up demand, and therefore the price of German bonds already issued and traded on the market.
Sovereign bonds carry an interest rate or yield which is fixed at issue for the life of the bond. If the price of the bond rises, as is the case for Germany, the fixed interest as a percentage of the increased price drops, signalling the rate Germany would have to pay to borrow new money.
The process works in reverse. Hence, if savers are increasingly reluctant to hold or to buy French or Spanish bonds for example, the price falls, and the fixed interest rises as a percentage, setting a new level for the next borrowing operation.